Chapter 2: Structure Of Atom – Class 11 Notes for NEET/JEE

🥰Learn Sufficient Notes🥰

---

1. Introduction to Atomic Structure

🔹 1. What is an Atom ?

An atom is the smallest unit of matter that cannot be broken further by chemical methods.
It makes up everything — solids, liquids, gases, even our own body!

🔹 2. History of Atom

• The idea of the atom came from ancient Indian and Greek philosophers.
• Democritus (Greek) said that matter is made up of tiny indivisible particles called “atomos”.
• In India, Maharishi Kanad also gave a similar idea — he called it “anu”.

🔹 3. Dalton’s Atomic Theory (1808)

John Dalton was a scientist who gave the first scientific atomic theory.
He said:

1. All matter is made of atoms.
2. Atoms are indivisible and indestructible.
3. All atoms of a given element are identical.
4. Atoms combine in fixed whole-number ratios to form compounds.
5. Chemical reactions involve rearrangement of atoms.

🟡 Note: Some points of Dalton’s theory are now outdated due to discovery of electrons, protons, and neutrons.

Also You Can Study With Our Notes Chapter 1- . Some Basic Concepts of Chemistry

🔹 4. Subatomic Particles

Later, scientists discovered that the atom is not indivisible — it has smaller parts:

Particle	Symbol	Charge	Mass (approx.)	Discovered by
Electron	e⁻	–1	1/1836 u	J.J. Thomson
Proton	p⁺	+1	1 u	Ernest Rutherford
Neutron	n⁰	0 (neutral)	1 u	James Chadwick

🔹 5. Modern Understanding of Atom

• An atom has two main parts:
  1. Nucleus – center part, contains protons and neutrons
  2. Electron cloud – electrons revolve around the nucleus in different paths or orbitals

🔹 6. Size of Atom

• Atoms are extremely small.
• Radius of an atom ≈ 10⁻¹⁰ m
• Radius of nucleus ≈ 10⁻¹⁵ m
  ➡️ This means the nucleus is 10,000 times smaller than the atom!

🔹 7. Mass of Atom

• Almost the entire mass of the atom is in its nucleus because electrons are very light.
• Unit of atomic mass is atomic mass unit (u) or dalton (Da).
  1 u = 1/12th of mass of carbon-12 atom.

🔹 8. Atomic Symbols and Numbers

• Atomic Number (Z) = Number of protons = Number of electrons (in neutral atom)
• Mass Number (A) = Number of protons + Number of neutrons
• Representation: ^A_Z​X
  • Example: ₆^12​C means Carbon has 6 protons and 6 neutrons

🔹 9. Isotopes, Isobars, Isotones

• Isotopes: Same atomic number, different mass number (e.g. ¹H, ²H, ³H)
• Isobars: Same mass number, different atomic number (e.g. ¹⁴C and ¹⁴N)
• Isotones: Same number of neutrons (e.g. ¹⁴C and ¹⁵N have 8 neutrons)

✅ Quick Summary:

Concept	Meaning
Atom	Smallest unit of matter
Dalton’s Theory	First scientific theory of atoms
Subatomic Particles	Electron, Proton, Neutron
Nucleus	Dense center of atom, contains p⁺ and n⁰
Electron Cloud	Region where e⁻ move around nucleus
Atomic Number (Z)	No. of protons (also electrons in neutral atom)
Mass Number (A)	Protons + Neutrons
Isotopes	Same Z, different A
Isobars	Same A, different Z
Isotones	Same number of neutrons

---

2. Discovery of Electron, Proton, and Neutron

🔹 1. Discovery of Electron

🧠 Discovered by: J.J. Thomson (1897)

🧪 Experiment: Cathode Ray Tube Experiment (Crookes Tube)

✅ Setup:

• A glass tube with low-pressure gas inside.
• Two metal plates (electrodes): Cathode (-) and Anode (+).
• High voltage (~10,000 volts) applied.

🔍 Observations:

• A greenish glow (fluorescent light) observed on the opposite wall.
• Rays travel from cathode to anode, so called “Cathode Rays”.
• These rays:
  • Cast shadow of objects placed inside the tube.
  • Get deflected by electric and magnetic fields, indicating they are negatively charged.
  • Can rotate a paddle wheel → they have mass.

🧾 Conclusions:

• Rays were made of tiny negatively charged particles → called Electrons.
• J.J. Thomson measured the charge-to-mass ratio (e/m) of electron:
  • e/m​ = 1.758×10¹¹ C/kg

🧪 Charge on Electron (by Millikan’s Oil Drop Experiment):

• Value of charge: e = 1.602 × 10⁻¹⁹ Coulombs
• Hence, mass of electron:
  • m= e /(e/m) ​=9.1×10⁻³¹ kg

🔹 2. Discovery of Proton

🧠 Discovered by: E. Goldstein (1886)

🧪 Experiment: Canal Ray Experiment

✅ Setup:

• Modified cathode ray tube with holes in cathode.
• Used hydrogen gas inside the tube.

🔍 Observations:

• Rays seen going in opposite direction to cathode rays (from anode to cathode).
• Called “Canal Rays” or “Anode Rays”.

🧾 Conclusions:

• These rays were made of positively charged particles.
• In hydrogen gas, only one proton per atom — hence the particle was named Proton.

📌 Properties of Proton:

Property	Value
Charge	+1 (1.602 × 10⁻¹⁹ C)
Mass	1.672 × 10⁻²⁷ kg (~1 u)
Symbol	p⁺

🔹 3. Discovery of Neutron

🧠 Discovered by: James Chadwick (1932)

🧪 Experiment: Bombarded beryllium with alpha particles

✅ Setup:

• Alpha particles (⁴He nuclei) fired at beryllium sheet.
• A new type of radiation was emitted — uncharged and penetrating.
• These rays knocked protons out from paraffin wax.

🔍 Observations:

• The radiation had mass but no charge.
• Could not be deflected by electric/magnetic fields → neutral in nature.

🧾 Conclusion:

• A new particle called neutron was discovered.
• It had no charge, but mass ≈ mass of proton.

📌 Properties of Neutron:

Property	Value
Charge	0 (neutral)
Mass	1.675 × 10⁻²⁷ kg (~1 u)
Symbol	n⁰

📊 Comparison Table of Subatomic Particles

Particle	Symbol	Charge	Mass (kg)	Relative Mass	Discovered By
Electron	e⁻	–1 (negative)	9.1 × 10⁻³¹	1/1836	J.J. Thomson
Proton	p⁺	+1 (positive)	1.672 × 10⁻²⁷	1	E. Goldstein
Neutron	n⁰	0 (neutral)	1.675 × 10⁻²⁷	1	James Chadwick

🧠 Key Points to Remember (NEET + JEE Focus):

Concept	NEET	JEE
Electron discovery	Important theory	+ Numericals (e/m ratio)
Millikan oil drop (charge)	Basic idea	Derivations may come
Proton and canal rays	Theory only	Basic questions
Neutron discovery	Theory only	Conceptual MCQs
Mass and charge of particles	Factual MCQs	Also used in numericals

---

3. 🧪 Thomson’s Atomic Model – Explained for NEET & JEE

🔹 Who Proposed the Model ?

• J.J. Thomson in 1904
• After discovering the electron in 1897, he tried to explain how these electrons are arranged inside the atom.

🔸 Background Before Thomson’s Model

• Scientists had discovered electrons (negatively charged particles), but:
  • Atom was electrically neutral
  • So, there must be positive charge to balance the electrons
• Thomson tried to explain this arrangement of positive and negative charges in an atom.

🍩 Thomson’s Model (Plum Pudding / Watermelon / Raisin Cake Model)

📖 Main Idea:

“Atom is like a spherical ball of positive charge with electrons embedded in it, like seeds in a watermelon or raisins in a pudding.”

📌 Key Postulates (Points):

No.	Postulate
1.	Atom is a uniform sphere of positive charge.
2.	Electrons are embedded in this positive sphere like raisins.
3.	Overall charge of atom is zero (neutral), because negative & positive charges balance.
4.	Mass of the atom is evenly spread out.

📊 Visual Representation:

Imagine:

• A big positively charged sphere
• Tiny negatively charged electrons scattered inside it like:
  • Raisins in pudding
  • Seeds in watermelon

🧠 Diagram of Thomson’s Model (Describe or draw in exam)

Just like Electrons In An Atoms:-        +         -         +
    -       +       -         +
       -         +       -
    +         -         +

(Big positive sphere with small negative electrons)

🔍 Example Analogy:

• Just like:
  • Pudding = positive charge
  • Raisins = negative electrons
• Atom = positive “dough” with negative “bits” scattered

✅ Successes of Thomson’s Model

• First model to explain:
  • Neutrality of atom
  • Presence of electrons
• Set the stage for further research

❌ Failures of Thomson’s Model

Reason	Why It Failed?
Couldn’t explain nucleus	Didn’t mention anything about a dense core in atom
No explanation for alpha scattering	Couldn’t explain results of Rutherford’s experiment
Didn’t explain energy levels	No idea about how electrons move or how energy is absorbed/emitted
Stability issue	Couldn’t explain how electrons stay embedded without moving or collapsing

🔬 Why was it rejected? (Rutherford’s Alpha Scattering Experiment)

• In 1909, Rutherford did the gold foil experiment, which showed:
  • Atom has a tiny, dense, positive nucleus
  • Most of the atom is empty space
• This totally contradicted Thomson’s model, so it was discarded.

🎯 NEET & JEE Exam Focus

Concept	NEET Exam	JEE Main/Advanced
Basic structure and idea	1–2 theory questions	1–2 theory + comparison questions
Name and analogy (plum pudding)	Often asked in assertion–reason	Sometimes in MCQs
Failures of the model	MCQs and comprehension	Conceptual + paragraph type Qs
Visual/Diagram based questions	Low chance	High chance in Advanced

🧠 Quick Summary Table: Thomson’s Atomic Model

Feature	Description
Discovered by	J.J. Thomson (1904)
Nickname	Plum Pudding / Watermelon Model
Atom Structure	Positive sphere with electrons embedded
Charge	Atom is neutral overall
Electrons	Fixed inside the positive mass like seeds
Main Limitation	No nucleus, no electron movement, instability
Rejected By	Rutherford’s Alpha Scattering Experiment (1909)

📌 Exam Tip:

Always connect Thomson’s model with what came before (Dalton’s) and after (Rutherford’s) to answer assertion-reason, timeline, or model-based questions.

---

4. Rutherford’s Nuclear Model & Alpha Scattering Experiment

🔹 1. Background

• After J.J. Thomson’s atomic model, there were many unanswered questions, such as:
  • Where is the positive charge exactly located?
  • Why do electrons not collapse into the nucleus?
• To answer these, Ernest Rutherford conducted a famous experiment in 1909.

🔬 2. Rutherford’s Alpha Particle Scattering Experiment

✅ Setup:

Part	Description
Source	Alpha particles (α) – ⁴₂He²⁺ nuclei (heavy, +2 charge)
Target	Thin gold foil (0.00004 cm thick)
Detector	Fluorescent screen coated with zinc sulfide (ZnS)
Observation Method	Wherever α-particles hit ZnS, tiny flashes (scintillations) appeared.

🧠 Why Alpha Particles?

• They are heavy, positively charged, and move at high speed.
• Good for testing the distribution of charge and mass inside atoms.

🔍 3. Observations by Rutherford

Observation	% Particles Affected
Most α-particles passed straight through the gold foil.	~99%
Some α-particles were deflected at small angles.	~0.1%
A very few were deflected at large angles or even bounced back.	~1 in 20,000

📌 4. Rutherford’s Conclusions

From the observations, Rutherford gave a new atomic model.

📖 Main Conclusions:

1. Atom is mostly empty space
   → Because most α-particles passed through without deflection.
2. Positive charge is concentrated in a small, dense region
   → Called the nucleus.
3. Nucleus is very small compared to the size of atom
   → Most of the atom’s volume is empty space.
4. Electrons revolve around the nucleus in circular paths → like planets around the sun.

🌐 5. Rutherford’s Atomic Model (Planetary Model)

“Atom consists of a positively charged dense nucleus at the center and electrons revolve around it in circular orbits.”

🧠 Key Features of Rutherford’s Model:

Feature	Description
Nucleus	Dense, heavy, positively charged core of the atom
Electrons	Revolve around nucleus in circular orbits
Atomic Size	Radius of nucleus ≈ 10⁻¹⁵ m ; Radius of atom ≈ 10⁻¹⁰ m (100,000× larger!)
Mass Distribution	Almost all mass of atom is in nucleus
Charge Distribution	Positive charge concentrated in nucleus

---

📊 Diagram of Rutherford’s Model

Like This-  e⁻              e⁻
       \          /
         \      /
        [ Nucleus ]
         /     \
      e⁻         e⁻
(Electrons revolving around a small central nucleus)

❌ 6. Limitations of Rutherford’s Model

Problem	Explanation
Stability issue	According to classical physics, revolving electrons should emit energy and spiral into nucleus — atom would collapse. But atoms are stable!
No explanation of energy levels	Didn’t explain why electrons don’t fall or how spectral lines (like hydrogen spectrum) are formed
Couldn’t explain hydrogen spectrum	Rutherford’s model failed to explain line spectra observed in emission/absorption

🧠 7. How Did Bohr Fix It Later?

• Niels Bohr modified Rutherford’s model by introducing:
  • Quantized energy levels
  • Electrons revolve in fixed orbits without radiating energy
• But that’s a separate topic! 😄

📌 Summary Table: Rutherford’s Nuclear Model

Feature	Description
Scientist	Ernest Rutherford
Year	1909 (experiment), 1911 (model)
Experiment	Alpha scattering with gold foil
Observations	Most α-particles passed; few deflected; very few rebounded
Nucleus	Tiny, dense, positively charged center of atom
Electrons	Revolve around nucleus like planets
Major Failure	Could not explain stability of atom or atomic spectra

📚 Quick Memory Hack:

• Empty space = Most α-particles went straight
• Tiny nucleus = Some deflected sharply
• Electrons revolve = Like planets
• Fails classically = Atom should collapse (but doesn’t!)

---

5. Bohr’s Atomic Model – Postulates, Radius, Energy, and Limitations

🔹 1. Background: Why Bohr’s Model ?

• Rutherford’s model introduced the nucleus and revolving electrons.
• But it failed to explain:
  • Why electrons don’t fall into the nucleus?
  • Why atoms emit line spectra (like Hydrogen)?
• So, in 1913, Niels Bohr proposed a new model of the atom.

🧠 2. Bohr’s Postulates (Main Assumptions)

🧾 Postulate 1: Stationary Orbits

Electrons revolve around the nucleus in certain fixed circular paths, called orbits or shells (n=1,2,3…).

• These are also called energy levels.
• While moving in these orbits, electrons don’t radiate energy → hence, atoms are stable.

🧾 Postulate 2: Quantization of Angular Momentum

Only those orbits are allowed where the angular momentum (L) of the electron is a whole number multiple of h/2π.

L = mvr = nh/2π​(where n = 1, 2, 3…)

• Here:
  • m = mass of electron
  • v = velocity
  • r = radius of orbit
  • h = Planck’s constant
  • n = orbit number or principal quantum number

🧾 Postulate 3: Emission or Absorption of Energy

Electron jumps from one orbit to another by absorbing or emitting a photon of energy.

ΔE=E₂ ​– E₁ ​=hν

• If electron goes to higher orbit → absorbs energy
• If it falls to lower orbit → emits energy
• ν = frequency of emitted/absorbed light

🌐 3. Important Formulas from Bohr’s Model (For Hydrogen-like Atoms)

Applies to Hydrogen (H), He⁺, Li²⁺… (i.e., single electron species)

✅ Radius of nth orbit (rₙ):

r_n​= n²h²ϵ₀​​/πme²Z = 0.529 × n²/Z​ × 10^-10

• n = orbit number
• Z = atomic number
• For hydrogen (Z=1):
  • r₁= 0.529 10^-10

✅ Velocity of electron (vₙ):

v_n​ = Ze²/2ϵ₀​h​ ⋅ 1/n​=2.18×10⁶ ⋅ Z/n m/s

✅ Energy of electron in nth orbit (Eₙ):

E _n​= me⁴Z²​/−8ϵ²​₀h²n² = −13.6 ⋅  Z²/n²​eV

• Negative sign shows the electron is bound to nucleus.

✅ Frequency of emitted/absorbed radiation:

ΔE = hν =13.6Z² (1/n²₁​1​ − 1/n²₂​​) eV

✅ Wave Number Formula (Rydberg’s Formula):

νˉ = RZ² (1/n²₁ – 1/n²₂​)

• R = 1.097 × 10⁷m⁻¹ (Rydberg constant)

🌈 4. Spectral Series in Hydrogen Atom (NEET + JEE Favourite)

Series Name	Transition To (n₁)	From (n₂)	Region
Lyman	1	2,3,4…	UV region
Balmer	2	3,4,5…	Visible light
Paschen	3	4,5,6…	Infrared
Brackett	4	5,6,7…	Infrared
Pfund	5	6,7,8…	Infrared

🎯 5. Success of Bohr’s Model

Point	Description
✅ Explained stability of atom	Electrons in stable orbits don’t radiate energy
✅ Explained hydrogen line spectrum	Balmer, Lyman, etc. series matched with observed values
✅ Introduced quantum concept	First model using quantization in atomic theory
✅ Mathematically accurate (for H)	Calculated energy levels match experiment (for H & H-like ions)

❌ 6. Limitations of Bohr’s Model

Problem Area	Limitation
🧪 Multi-electron atoms	Could not explain spectra of atoms with more than 1 electron
🧲 Zeeman/Stark Effect	Couldn’t explain splitting of lines in magnetic/electric fields
↻ Circular orbits	Assumed fixed circular orbits — contradicts quantum mechanics
📦 Heisenberg’s Principle	Violates uncertainty principle (precise path + momentum together)
❌ Doesn’t explain intensities	Why some spectral lines are brighter/weaker — not explained

🧠 7. Summary Table: Bohr’s Atomic Model

Feature	Description
Scientist	Niels Bohr (1913)
Electrons	Revolve in fixed orbits (n=1,2,3…)
Energy	Quantized; only certain levels allowed
Jumping Electron	Emits or absorbs light when changing orbits
Radius of Orbit (rₙ)	∝ n²/Z
Energy of Orbit (Eₙ)	∝ -Z²/n²
Successfully Explained	Hydrogen spectrum, atomic stability
Limitations	Doesn’t work for complex atoms, violates modern principles

✅ Quick Revision Memonic (for Series):

Let’s Buy Pizza Before Party
(Lyman, Balmer, Paschen, Brackett, Pfund)

---

6. Shells and Subshells

🔹 1. What are Shells ?

• Electrons in an atom revolve in different energy levels or orbits around the nucleus.
• These orbits are called electron shells.

✅ Shells are denoted by :

Shell Name	Symbol	Principal Quantum Number (n)
K-shell	n = 1	1st energy level
L-shell	n = 2	2nd energy level
M-shell	n = 3	3rd energy level
N-shell	n = 4	4th energy level

• The value of ‘n’ (principal quantum number) determines the energy of that shell.

📌 Important Properties of Shells :

• Lower n = Lower energy
• Number of electrons in a shell = 2n22n^22n2

Shell	n	Max Electrons = 2n²
K	1	2
L	2	8
M	3	18
N	4	32

🔸 2. What are Subshells ?

• Each shell is further divided into subshells based on the azimuthal quantum number (ℓ).
• Subshells are regions within a shell where electrons of particular energy and shape are found.

✅ Types of Subshells :

Subshell	Symbol	Azimuthal Quantum Number (ℓ)	Max Electrons
s	ℓ = 0	Spherical shape	2
p	ℓ = 1	Dumbbell shape	6
d	ℓ = 2	Cloverleaf shape	10
f	ℓ = 3	Complex shape	14

📘 Subshells within Each Shell:

Shell (n)	Subshells Present
1 (K)	1s
2 (L)	2s, 2p
3 (M)	3s, 3p, 3d
4 (N)	4s, 4p, 4d, 4f

• Subshells increase with n and follow this pattern.

🧪 3. How Many Orbitals in Each Subshell ?

Each subshell contains a set number of orbitals, and each orbital holds 2 electrons.

Subshell	Orbitals	Electrons (2 per orbital)
s	1	2
p	3	6
d	5	10
f	7	14

---

🧠 4. Full Shell–Subshell Structure Example

Let’s see how shells and subshells work together using examples:

🔹 Hydrogen (Z = 1):

• Shell: K (n=1)
• Subshell: 1s → 1 electron

🔹 Oxygen (Z = 8):

• Shells: K (n=1), L (n=2)
• Subshells:
  • 1s² (2 electrons)
  • 2s² (2 electrons)
  • 2p⁴ (4 electrons)
• Total = 8 electrons

🔄 5. Order of Filling Subshells (Aufbau Principle)

Electron filling is based on increasing energy:

In This Manner-
2s
2p
3s
3p
4s
3d
4p
5s
4d
5p
6s
...

You can use the “diagonal rule” to remember this:

Like This-      1s
       ↓
       2s → 2p
       ↓     ↓
       3s → 3p → 4s
       ↓     ↓     ↓
       3d → 4p → 5s
       ↓     ↓     ↓
       4d → 5p → 6s
       ↓     ↓     ↓
       4f → 5d → 6p
       ↓     ↓     ↓
       6d → 7p → 8s

🔍 6. Quick Summary Table: Shells vs Subshells

Feature	Shell	Subshell
Defined by	Principal quantum number (n)	Azimuthal quantum number (ℓ)
Denoted by	K, L, M, N (or n = 1, 2, …)	s, p, d, f
Energy Level	Increases with n	Varies within same n
Max Electrons	2n²	s = 2, p = 6, d = 10, f = 14
Shape	Not specified	s = spherical, p = dumbbell, etc.

🎯 NEET + JEE Focus Tips

Topic	NEET Level	JEE Level
Shell & Subshell basics	Must know names, max e⁻ count	Must know quantum number logic
Aufbau Rule	Frequently asked in MCQs	May test exceptions (Cr, Cu etc)
Orbitals in each subshell	Direct questions	Orbital diagrams asked
Quantum numbers	Important	Conceptual + formula based Qs

📌 Quick Revision Points:

• Shell = main energy level (n = 1,2,3…)
• Subshell = division of shell (s, p, d, f)
• Each subshell has orbitals (s=1, p=3, d=5, f=7)
• Max electrons in orbital = 2
• Max in subshell = orbitals × 2

---

7. 🌟 Dual Nature of Matter – de Broglie Equation

🔹 1. What is Dual Nature of Matter?

According to modern physics, matter (like electrons) exhibits both:

• Particle-like properties (mass, momentum)
• Wave-like properties (wavelength, interference)

🧠 This concept is known as the dual nature of matter.

🔍 2. Background: Wave Nature of Light

Before understanding matter’s duality, remember:

• Light was once considered only a wave.
• But Einstein proved it also behaves like a particle (photon).
• So, light shows dual nature — both wave and particle behavior.

👉 Then came a big question:
💡 If light (wave) can behave like a particle, can particles (like electrons) behave like waves?

👨‍🔬 3. Louis de Broglie’s Hypothesis (1924)

• Louis de Broglie, a French physicist, proposed that:

“All material particles, like electrons, have wave properties.”

🔁 Wave–Particle Duality for Matter:

• Moving particles (like electrons, protons) are associated with waves → called de Broglie waves or matter waves.

🧮 4. de Broglie Equation:

The wavelength (λ) of a moving particle is given by:- λ  = h/​mv

Where:

• λ = de Broglie wavelength (in meters)
• h = Planck’s constant = 6.626×10⁻³⁴  Js
• m = mass of the particle (in kg)
• v = velocity of the particle (in m/s)

➡️ Also written as: λ = h/p ​(since momentum p = mv)

🧠 5. Key Concepts from de Broglie Equation

Concept	Explanation
Particle mass ↑	Wavelength ↓ (heavier particles have shorter wavelengths)
Particle speed ↑	Wavelength ↓ (faster particles have shorter wavelengths)
Only moving objects	Matter waves are associated only with moving particles
Massless particles (like photons)	Also show wave nature, but follow different rules

🧪 6. Applications of de Broglie Concept

🔬 Electron Diffraction Experiments:

• When a beam of electrons is passed through a crystal or slit, it shows interference and diffraction, just like waves.
• This proved experimentally that electrons (particles) behave like waves.

💡 Bohr’s Quantization Justified:

• de Broglie explained why only certain orbits are allowed in Bohr’s model.
• He said: Electron’s orbit must contain an integer number of wavelengths.

2πr = nλ ⇒ 2πr = nh​/mv​

✔️ This matches Bohr’s quantized angular momentum.

📚 7. de Broglie Wavelength – Numerical Example

Q: Find de Broglie wavelength of an electron moving at 2×10⁶ m/s.
(Mass of electron =9.1×10⁻³¹ kg)

Answer- λ=  6.626 × 10⁻³⁴ /9.1×10⁻³¹ ×2 × 10⁶ ​=  3.64×10⁻¹⁰m

🟢 Comparable to X-ray wavelength → shows wave behavior.

🚫 8. Limitations of de Broglie Concept

Limitation	Explanation
Not observable for large bodies	Wavelength becomes extremely small for heavy objects (like a ball)
No explanation of wave source	Doesn’t explain why matter shows wave properties
Works only for microscopic particles	Only meaningful for electrons, protons, etc.

🔄 9. Difference: Classical vs Quantum View

Property	Classical Physics	Quantum Physics (de Broglie)
Particle Nature	Mass, position, momentum	Also has wave-like properties
Wave Nature	Light is wave only	Light and matter both have dual nature
Orbitals	Electrons revolve like planets	Electrons exist in wave-like orbitals

🧠 10. Quick Revision Summary

Topic	Formula / Point
de Broglie Equation	λ=h/mv
Planck’s constant	h=6.626×10−34  Js
de Broglie for photon	λ = h/p​ =  hc​/E
Wavelength vs mass/velocity	Inversely proportional
Evidence	Electron diffraction, Bohr’s orbits

🎯 NEET + JEE Tips

For NEET	For JEE
Memorize formula λ=h/mv	Must know derivation logic + numerical Qs
Know wave-particle duality concept	Practice logic-based conceptual Qs
Application to electron only	Questions on proton, neutron may appear
Simple numericals expected	Detailed numericals and application-based Qs

📝 Extra Concept: de Broglie for Photon

If a particle has no mass (like a photon), then: λ= hc​/E ​(where E=hν)

---

8. 🌟 Heisenberg’s Uncertainty Principle

🔹 1. What is This Principle?

This principle says:

“We can’t know the exact position and exact speed (momentum) of a tiny particle (like an electron) at the same time.”

⚠️ If we know where the electron is, we cannot know how fast it’s going and vice versa.

🔹 2. Why is This Important ?

In our daily life, we can easily find where a car is and how fast it’s going.

But with very small particles like electrons, it’s not possible.

When we try to see or measure an electron:

• We shine light (photons) on it.
• That light hits the electron and changes its speed or position.

So, just by looking at it, we disturb it.

🔹 3. The Formula:

The uncertainty principle is written as:  Δx ⋅ Δp ≥  h​/4π

Meaning:

• Δx = how uncertain the position is
• Δp = how uncertain the momentum (mass × velocity) is
• h = Planck’s constant = 6.626 × 10⁻³⁴ Js

➡️ If you try to make position more accurate, momentum becomes less accurate.

🔹 4. Real-Life Example

Imagine you’re in a dark room and trying to find a ball with a flashlight.

• You shine the light → now you see the ball.
• But when light hits it, the ball moves a little.

So now:

• You saw the ball’s position.
• But because it moved, you can’t tell how fast it was going earlier.

This is just like electrons!

🔹 5. Why Is It Important in Chemistry ?

It explains:

• Why electrons don’t follow fixed circular paths (like Bohr said).
• Instead, they are in cloud-like areas called orbitals.
• We can only say: “There is a high chance of finding the electron here.”

So, quantum mechanics is based on probability, not certainty.

🔹 6. Simple Summary Table

Term	Meaning
Position (Δx\Delta xΔx)	Where the particle is
Momentum (Δp\Delta pΔp)	Mass × Speed of the particle
Uncertainty	We can’t know both exactly at the same time
Formula	Δx ⋅ Δp ≥  h​/4π
Importance	Explains why electrons don’t have fixed orbits

🔹 7. Important Points for NEET/JEE

✅ No need to remember derivation — just the formula, but understand the derivation is important.
✅ Understand why electrons don’t stay in fixed orbits.
✅ This supports the modern model of atom (quantum model).

🔹 8. Key Takeaways

• Electrons are very small and fast.
• We cannot know both position and speed at the same time.
• This is not because our tools are weak — it’s because nature works this way.
• Electrons move in orbitals (clouds), not fixed paths.

---

9. 🌌 Quantum Mechanical Model of Atom

🔹 1. What is Quantum Mechanical Model ?

This is the modern model of an atom.
It is based on:

• Heisenberg’s Uncertainty Principle
• de Broglie’s Wave Nature of Electrons
• Schrödinger’s Wave Equation

⚠️ Unlike Bohr’s model (which said electrons move in fixed circular paths), this model says:

Electrons are found in cloud-like areas called “orbitals,” not fixed orbits.

🔹 2. Why Was This Model Needed ?

Bohr’s model failed to explain:

• Multielectron atoms
• Shapes of molecules
• Why only certain orbitals are allowed

So, scientists developed this model using quantum mechanics (the science of very small particles).

🔹 3. Main Features of the Quantum Mechanical Model

Feature	Explanation
🔬 Electrons behave like waves	(From de Broglie)
🚫 We can’t know position & momentum exactly	(From Heisenberg)
📊 Electron’s behavior is probabilistic	Not fixed paths, only chances
🌀 Schrödinger’s Equation used	To calculate where electron is most likely to be
☁️ Electrons are in orbitals	Not orbits; they are 3D regions where electron is likely to be found

🔹 4. Schrödinger’s Wave Equation (Basic Idea)

Erwin Schrödinger gave a mathematical equation that describes the wave behavior of an electron: H^{^}Ψ = EΨ

Don’t worry! You don’t have to solve it in NEET or JEE.

✅ Just understand:

• Ψ\PsiΨ (psi) = wave function
• Ψ2\Psi^2Ψ2 = probability of finding the electron

Wherever Ψ2\Psi^2Ψ2 is large → electron is likely to be found there

This region = orbital

🔹 5. What Are Orbitals ?

Orbitals are 3D regions around the nucleus where the probability of finding the electron is high (about 90-95%).

Important Points:

Orbital	Description
☁️ Not fixed path	It’s a cloud-like region
🧊 Each orbital has shape	s = spherical, p = dumbbell, etc.
🎯 Maximum 2 electrons	Can stay in one orbital with opposite spins

🔹 6. Differences: Bohr’s Orbit vs. Quantum Orbital

Bohr’s Orbit	Quantum Orbital
Fixed circular path	3D cloud-like region
Definite position & speed	Only probability known
Classical physics based	Quantum mechanics based
Works only for H atom	Works for all atoms

🔹 7. What This Model Explains:

• Why electrons don’t crash into the nucleus
• How atoms absorb/release energy
• Shapes of orbitals (s, p, d, f)
• Energy levels and sublevels
• Rules like Aufbau, Hund, Pauli (for electron filling)

🔹 8. Key Summary Table

Concept	Meaning
Wave Nature	Electrons behave like waves (de Broglie)
Uncertainty	Can’t know both position and speed (Heisenberg)
Wave Equation	Schrödinger gave equation to find electron’s behavior
Orbital	3D region where electron is likely to be
Probability Concept	No fixed path, only chances
Orbitals vs Orbits	Orbitals = modern; Orbits = outdated

🔹 9. Real-Life Analogy (To Understand Easily)

Imagine a bee flying around a flower:

• It doesn’t follow one fixed circle.
• It moves randomly in the area.
• You can’t say exactly where it is at one moment.

But you can say: “It is usually around this flower.”

This is like an electron in an orbital!

🔹 10. NEET + JEE Important Points

NEET Aspirants	JEE Aspirants
Understand orbitals are clouds, not paths	Understand Schrödinger’s equation conceptually
Learn shapes of orbitals (s, p, d)	Practice electron configuration and quantum numbers
Focus on probabilistic nature of electrons	Be ready for numerical + conceptual questions

🔹 11. Keywords to Remember

• Wave function (ψ) = Mathematical description of electron
• ψ² = Probability density
• Orbital = Region where electron is likely to be found
• Quantum Mechanics = Math + rules for tiny particles like electrons

🧠 Final Takeaways:

✅ Quantum model is the most accurate atomic model so far.
✅ Based on mathematics, probability, and waves.
✅ It replaces the idea of fixed paths with cloud-like orbitals.

---

10. 🔮 Schrödinger’s Wave Equation

🔹 1. What Is Schrödinger’s Wave Equation ?

It is a mathematical equation that describes the behavior of an electron as a wave.

This idea came from:

• de Broglie’s theory: Electrons behave like waves
• Heisenberg’s uncertainty: We can’t find exact location of electrons
• So, instead of “where” electron is, we talk about “where it is likely to be”

Schrödinger ne bola:

“Let’s treat the electron like a wave, and use mathematics to find where it might be found.”

🔹 2. The Equation (Don’t Panic 😅)

 H^{^}Ψ=EΨ

Here:

• H^ = Hamiltonian operator (energy of the system)
• Ψ (Psi) = wave function
• E = total energy of the electron

📌 You don’t need to solve this equation in NEET/JEE — just understand what it means.

🔹 3. What is Wave Function (Ψ) ?

• It is a mathematical function.
• It does NOT have a direct physical meaning.
• But when you square it: Ψ2=Probability density\Psi^2 = \text{Probability density}Ψ2=Probability density This tells: What is the chance of finding an electron at a particular location?

🔹 4. Physical Meaning of Ψ and Ψ²

Symbol	Meaning	Physical Interpretation
Ψ	Wave function	No physical meaning directly
Ψ2	Probability density	High value → high chance of finding electron

🔹 5. What Did Schrödinger’s Equation Do?

• Gave us orbitals (regions where electron is most likely to be)
• Predicted energy levels of electrons in an atom
• Helped us understand shapes of orbitals (s, p, d, f)
• Replaced Bohr’s fixed orbits with probability clouds

🔹 6. Orbitals: What We Get from Schrödinger

Schrödinger’s equation tells us:

Output	Meaning
Orbitals	3D regions of high electron probability
Energy levels	Energy of each electron in each orbital
Shapes of orbitals	s = sphere, p = dumbbell, etc.
Orientation	Direction in space (like px, py, pz)

🔹 7. Visual Understanding

Imagine you’re trying to find a bee in a garden:

• You don’t know its exact location.
• But if you observe for long time, you’ll notice:
  👉 “The bee is usually near this flower.”

That’s like Ψ²2: It gives you a probable location, not exact.

Same with electrons in atoms. We don’t know exactly where they are — but we know where they’re likely to be.

🔹 8. Summary Table – What You Should Remember

Concept	Key Point
Schrödinger’s Equation	Describes wave nature of electrons
Ψ (psi)	Wave function (mathematical)
Ψ²	Probability of finding the electron
Output of equation	Orbitals, shapes, energies
Supports modern atom model	Based on quantum mechanics
Fixed paths replaced by orbitals	Electron clouds, not orbits

🔹 9. NEET & JEE Specific Points

NEET Focus	JEE Focus
No derivation needed	Understand concepts deeply
Know meaning of Ψ and Ψ²	Know how orbitals come from this
Understand orbitals and their energy	May ask conceptual/numerical questions

🔹 10. Final Thoughts

✅ Schrödinger’s equation is the heart of modern atomic theory.
✅ It treats the electron as a wave, not just a particle.
✅ We don’t get fixed paths but probability zones = orbitals
✅ This theory matches experimental results = it works!

---

11. Quantum Numbers (Principal, Azimuthal, Magnetic, Spin)

🔹 What are Quantum Numbers?

Quantum numbers are like a unique address for every electron inside an atom.
They tell us:

• Electron is in which shell
• Electron is in which shape of orbital
• Orbital is pointing in which direction
• Electron is spinning in which way

🔹 Total 4 Quantum Numbers:

No.	Name of Quantum Number	Symbol	Tells About…
1.	Principal Quantum Number	n	Shell / energy level
2.	Azimuthal Quantum Number	l	Subshell / orbital shape
3.	Magnetic Quantum Number	ml	Direction of orbital
4.	Spin Quantum Number	ms	Direction of electron spin

✅ 1. Principal Quantum Number (n)

• Tells the main shell of the electron (like 1st shell, 2nd shell)
• Values: 1, 2, 3, 4, …
• Bigger nnn means:
  • Electron is farther from the nucleus
  • Electron has more energy

n	Shell	Name
1	K	Lowest energy
2	L	Medium energy
3	M	Higher
4	N	Higher

✅ 2. Azimuthal Quantum Number (l)

• Tells the shape of orbital
• Values: 0 to (n – 1)

l	Subshell	Shape
0	s	Sphere
1	p	Dumbbell
2	d	Clover
3	f	Complex

👉 Example: If n = 3, then l = 0,1,2 → means s, p, d orbitals are possible.

✅ 3. Magnetic Quantum Number (mₗ)

• Tells the direction in which the orbital is pointing
• Values: from −l to +l

l (shape)	Possible mₗ values	No. of Orbitals
0 (s)	0	1
1 (p)	-1, 0, +1	3
2 (d)	-2 to +2	5
3 (f)	-3 to +3	7

✅ 4. Spin Quantum Number (mₛ)

• Tells the spin direction of electron (up or down)
• Only 2 values:
  • +1/2​ → clockwise spin
  • -1/2​ → anticlockwise spin

👉 In 1 orbital, only 2 electrons can stay — and both must have opposite spins.

🔹 Example: Oxygen Atom (Z = 8)

Electron configuration:
1s² 2s² 2p (Here 2,2,4 are electrons, oxygen has 8 electrons)
Last electron is in 2p orbital.

Quantum Number	Value	Meaning
n	2	2nd shell (L)
l	1	p orbital (shape)
mₗ	-1/0/+1 (any)	Direction
mₛ	+½ or −½	Spin direction

🔹 Summary Table

Quantum Number	Symbol	Tells Us
Principal	n	Energy level / shell
Azimuthal	l	Orbital shape (s, p, d, f)
Magnetic	mₗ	Orbital’s direction in space
Spin	mₛ	Electron spin (+½ or −½)

💡 Easy Trick:

Quantum Numbers = Electron’s Full Address!

Like:
🏠 Country (n) → City (l) → Street (mₗ) → Flat Number (mₛ)

🎯 NEET & JEE Tips:

For NEET	For JEE
Understand meaning of each quantum number	Learn how to write full set of 4 numbers
Know the shapes (s, p, d, f)	Solve basic MCQs with configuration
Don’t worry about derivations	Know value rules and restrictions

---

12. Shapes of s, p, d Orbitals (basic shape understanding)

Understanding the shapes of orbitals is a key part of Class 11 Chemistry. Orbitals are regions around the nucleus where the probability of finding an electron is highest. Different orbitals have different shapes, and these shapes help us understand how electrons are arranged in atoms.

In this article, we will explore the shapes of s, p, and d orbitals in simple and easy language — especially for NEET and JEE aspirants.

What is an Orbital?

An orbital is a three-dimensional space around the nucleus of an atom where the probability of finding an electron is maximum. Each orbital has a unique shape and orientation in space.

1. s-Orbital – Spherical Shape

• The s-orbital is spherical in shape.
• It is like a round ball or globe.
• The electron cloud is spread equally in all directions.

Key Points:

• Each energy level has only one s-orbital (e.g., 1s, 2s, 3s…).
• The shape remains the same, but the size increases with higher energy levels.
• s-orbitals do not have directionality.

Electrons held: Maximum 2 electrons in each s-orbital.

2. p-Orbitals – Dumbbell Shape

• p-orbitals look like dumbbells or two balloons joined at the center.
• They have two lobes on either side of the nucleus.

Orientations:

There are three p-orbitals:

• P_x​ – along the x-axis
• P_y​ – along the y-axis
• P_z​ – along the z-axis

These orbitals are identical in shape and energy but differ in direction.

Key Points:

• p-orbitals begin from the second shell (n = 2).
• Each p-orbital can hold 2 electrons → Total 6 electrons in all three p-orbitals.
• Directional in nature (along x, y, and z axes).

3. d-Orbitals – Cloverleaf & Ring Shapes

• d-orbitals have complex shapes.
• Most look like clover leaves (four lobes), and one has a dumbbell with a ring (doughnut shape).

Types of d-Orbitals:

1. d_xy
2. d_yz
3. d_zx
4. dx²-y²​
5. dz²(dumbbell with a ring)

Key Points:

• d-orbitals start from the third energy level (n = 3).
• There are five d-orbitals in each shell from n = 3 onwards.
• Each orbital can hold 2 electrons → Total 10 electrons in d-sublevel.
• The shape helps explain properties of transition elements.

Summary Table: s, p, d Orbitals

Orbital Type	Shape	No. of Orbitals	Max Electrons	Starts From
s	Spherical	1	2	n = 1
p	Dumbbell	3(px,py,pz)	6	n = 2
d	Cloverleaf/Doughnut	5	10	n = 3

Quick Comparison:

Feature	s-Orbital	p-Orbital	d-Orbital
Shape	Sphere	Dumbbell	Cloverleaf / Ring
Number of Orbitals	1	3	5
Directionality	None	Along x, y, z	Complex orientations
Maximum Electrons	2	6	10
Starts from Shell	n = 1	n = 2	n = 3

Important Tips for NEET & JEE

Final Words

Understanding the shapes of orbitals helps in knowing how electrons are arranged and how atoms bond with each other. Always remember:

• s is simple and spherical,
• p is dumbbell-shaped and directional,
• d is complex and clover-like.

• NEET Aspirants: Focus on basic shapes and number of orbitals.
• JEE Aspirants: Also learn names like dxy​,dz²​ and their orientations.
• No need to draw exact diagrams in most questions, but understand the concept well.

---

13. Probability Density (ψ²) and Radial Distribution (for JEE)

🧪 What is ψ (Psi) in Quantum Mechanics?

• In quantum mechanics, ψ (psi) is the wave function.
• It gives information about the state of an electron in an atom.
• ψ itself has no physical meaning.

But when we square it, we get something useful.

🌌 What is Probability Density (ψ²)?

• ψ² (psi squared) means the square of the wave function.
• It gives the probability density, i.e., how likely it is to find an electron at a specific point in space.

📌 Meaning:

• High ψ² → High chance of finding an electron there.
• Low ψ² → Low chance.
• ψ² is always positive (because it’s a square).

So, Probability Density = ψ² = likelihood of finding electron per unit volume at a point.

🎯 Visual Example (Imagine This):

Imagine the atom is a foggy cloud:

• Where the fog is thicker, the probability density is higher.
• Where it’s lighter, the probability is lower.
  That “thickness” at each point is like ψ².

🌀 Radial Probability and Radial Distribution Function

Even though ψ² tells us probability at a point, we are often more interested in the overall probability in a shell (a circular region at a distance from the nucleus).

That’s where Radial Distribution Function helps.

📈 What is Radial Probability Distribution?

• It tells us the total probability of finding an electron at a particular distance (radius r) from the nucleus.
• It is calculated by:

Radial Probability = ψ²⋅4πr²

🔍 Why Multiply by 4πr² ?

• Because 4πr² is the surface area of a spherical shell at distance r.
• It converts point-wise probability (ψ²) into total probability in a spherical shell.

🧠 Simple Difference Between ψ² and Radial Distribution:

Concept	ψ² (Probability Density)	Radial Distribution Function
Meaning	Probability per unit volume at a point	Total probability in a spherical shell
Depends on	ψ (wave function)	ψ² and distance (r)
Mathematical Term	ψ²	ψ² × 4πr²
Use	For point-wise electron probability	For radial zones like shells
Graph Shape	Peaks at center for s-orbital	Peak is not at center (more later)

📉 Radial Distribution Graph for 1s Orbital

For 1s orbital (Hydrogen-like atom):

• ψ² is maximum at the nucleus.
• But radial distribution is zero at nucleus, then increases, and then peaks at a certain distance.

That means:

• Although ψ² is highest at the nucleus, the space near the nucleus is very small.
• So the total probability becomes maximum a little away from nucleus.

📊 Graph Summary:

• x-axis: Distance from nucleus (r)
• y-axis: Radial probability

Region	Behavior
At nucleus (r = 0)	ψ² is maximum, but radial distribution is zero
At small distance	ψ² still high, and area increases → radial distribution increases
At peak distance	Radial distribution is maximum
Far away	ψ² becomes small, radial distribution falls

✅ Important Points for JEE:

• ψ² is the probability density, gives idea at a point.
• Radial distribution considers area at each shell (4πr²).
• Radial probability for 1s orbital is maximum at ~0.53 Å (Bohr radius).
• For higher orbitals (2s, 3s):
  • Graph has more than one peak (called nodes).
  • The number of nodes = n – l – 1

📌 Definitions (JEE-style):

1. Wave Function (ψ): A mathematical function describing the behavior of an electron in an atom.
2. Probability Density (ψ²): Square of the wave function; represents the likelihood of finding an electron at a point in space.
3. Radial Probability Distribution: Probability of finding an electron at a specific distance (r) from the nucleus in a spherical shell.
4. Radial Node: A distance from the nucleus where the radial probability becomes zero.

✍ Example Question for JEE:

Q: In the hydrogen atom, the maximum radial probability for the 1s orbital occurs at:

• (A) r = 0
• (B) r = ∞
• (C) r = a₀
• (D) r = 2a₀

Answer: ✅ (C) r = a₀ (Bohr radius)

📎 Final Summary Table:

Term	Meaning	Depends On
ψ (Wave Function)	Mathematical function (no meaning)	n, l, m, r
ψ² (Probability Density)	Electron density at a point	ψ
Radial Distribution	Total probability in a spherical shell	ψ², 4πr²
Radial Node	Point where radial probability is zero	Quantum numbers

---

14. 📘 Aufbau Principle

🔷 What is the Aufbau Principle?

The Aufbau Principle explains how electrons are filled in atomic orbitals when building up an atom.

The word “Aufbau” is German for “building up”.

🧠 Definition (Simple):

Electrons enter orbitals starting from the lowest energy level, and go to higher energy orbitals step-by-step.

📌 Why is the Aufbau Principle Important?

Because atoms are most stable when their electrons are in the lowest energy arrangement.
This rule helps us write the correct electronic configuration of any atom.

⚛️ Basic Rules of the Aufbau Principle:

1. Electrons fill orbitals in order of increasing energy.
2. Lower energy orbitals fill before higher energy ones.
3. The order of orbital filling is based on (n + l) rule.

📐 (n + l) Rule – The Key to Order

To find which orbital fills first, calculate the value of n + l:

• n = principal quantum number (main shell: 1, 2, 3,…)
• l = azimuthal quantum number (s = 0, p = 1, d = 2, f = 3)

🧮 How It Works:

• Lower (n + l) → lower energy
• If (n + l) is same for two orbitals, the orbital with lower n fills first

• 3d → n = 3, l = 2 → (n + l) = 5
• 4s → n = 4, l = 0 → (n + l) = 4

➡️ 4s has lower energy than 3d → So, 4s fills before 3d

📊 Order of Orbital Filling (According to Aufbau Principle)

Here’s the correct order in which orbitals are filled:

Like This- 
2s  
2p  
3s  
3p  
4s  
3d  
4p  
5s  
4d  
5p  
6s  
4f  
5d  
6p  
7s  
5f  
6d  
7p

➡️ You can remember this using diagonal rule chart or mnemonic tricks.

📷 Visual Diagram (Diagonal Rule)

Want an image of this? I can generate a diagonal arrow chart for you too!

Some elements do not follow the expected order completely due to extra stability of half-filled or fully-filled orbitals.

Most Common Exceptions:

• Chromium (Cr):
  Expected: [Ar] 4s² 3d⁴
  Actual: [Ar] 4s¹ 3d⁵ ✔️ (half-filled d orbital is more stable)
• Copper (Cu):
  Expected: [Ar] 4s² 3d⁹
  Actual: [Ar] 4s¹ 3d¹⁰ ✔️ (fully-filled d orbital is more stable)

These happen due to exchange energy and symmetry stability.

🧠 Summary Table:

Rule	Explanation
Aufbau Principle	Fill from lower to higher energy orbitals
(n + l) Rule	Lower (n + l) = lower energy
Exceptions	Cr, Cu, etc. → due to stable half/full-filled d
Electron Configuration Uses	Aufbau + Pauli + Hund’s Rule

💡 Tips for JEE/NEET:

• Remember the orbital order till at least 6p.
• Practice writing electronic configurations up to atomic number 30.
• Be careful with transition elements — learn their exceptions.
• Always use (n + l) rule if confused.

Q: Which of the following orbitals will fill first?

• (A) 4s
• (B) 3d
• (C) 4p
• (D) 5s

Ans: ✅ (A) 4s (It has lower (n + l) value than 3d)

---

15. 🧲 Pauli’s Exclusion Principle

🔍 What is Pauli’s Exclusion Principle?

Pauli’s Exclusion Principle is a fundamental rule in quantum mechanics, given by Wolfgang Pauli in 1925.

✅ Statement:

“No two electrons in the same atom can have the same set of four quantum numbers.”

This means that every electron in an atom must be unique in terms of its quantum identity.

To describe the position and properties of an electron, four quantum numbers are used:

Quantum Number	Symbol	What it Describes	Possible Values
Principal	n	Energy level/shell	1, 2, 3, …
Azimuthal	l	Subshell shape (s, p, d, f)	0 to (n−1)
Magnetic	ml	Orientation of orbital	–l to +l
Spin	ms	Spin of electron	+½ or –½

According to Pauli, two electrons can never have the same values for all four quantum numbers simultaneously.

🧪 Why is This Important?

The principle explains:

• Why each orbital can hold a maximum of two electrons
• Why those two electrons must have opposite spins (+½ and –½)
• The structure of the periodic table
• The way electrons are arranged in atoms

🔁 Pauli’s Principle and Orbital Filling

Example 1: Helium (Z = 2)

• Electron configuration: 1s²
• Both electrons are in the 1s orbital
• First electron:
  n = 1, l = 0, ml = 0, ms = +½
• Second electron:
  n = 1, l = 0, ml = 0, ms = –½
  ✅ All quantum numbers are the same except spin, so this is allowed.

Example 2: Violation

If both electrons in the same orbital had:

• n = 1, l = 0, ml = 0, ms = +½
• n = 1, l = 0, ml = 0, ms = +½
  ❌ This is not allowed as all quantum numbers are identical.

🎓 Analogy: Cinema Seat Example

Imagine a cinema hall where each seat (orbital) allows only 2 people (electrons).

• Both people must have different ID cards (quantum numbers)
• If one person already occupies a seat with a specific ID (quantum identity), the next person must differ at least in one ID field (spin)

🧬 Link with Electron Configuration

The Pauli principle helps determine:

• How electrons are filled in orbitals
• The maximum number of electrons per orbital (2)
• The structure of electron shells and subshells

🧠 Key Insights for JEE/NEET

Concept	What It Tells You
1 orbital = max 2 electrons	Because spins must be opposite
Every electron is unique	Each has a unique combination of quantum numbers
Explains structure of atoms	Especially the periodic table layout
Applies to all fermions	Not just electrons but also protons and neutrons

📊 How Pauli’s Principle Shapes the Periodic Table

The Pauli Exclusion Principle is why the periodic table is structured the way it is. Because:

• Electrons are filled into orbitals one by one
• No two electrons in the same atom can be identical
• This causes a predictable electron configuration pattern

🔄 Pauli vs Hund vs Aufbau – Know the Difference

Rule	What It Means
Pauli’s Exclusion	No 2 electrons can have the same 4 quantum numbers
Hund’s Rule	In degenerate orbitals, electrons occupy separately with parallel spins
Aufbau Principle	Orbitals are filled in the order of increasing energy

📝 Sample Questions (JEE & NEET Practice)

🔹 MCQ 1:

Q: How many electrons can occupy the 3p orbital?

A: 6 (3p has 3 orbitals × 2 electrons each = 6)

🔹 MCQ 2:

Q: Which of the following violates Pauli’s Exclusion Principle?
A) 1s²
B) 2s²
C) 2p⁷
D) 3d¹⁰

Answer: C) 2p⁷ (p-subshell can hold a maximum of 6 electrons)

✅ Final Summary – Quick Revision

• Each electron in an atom is identified by 4 quantum numbers.
• No two electrons can have the same set of these 4 quantum numbers.
• Each orbital holds maximum 2 electrons with opposite spins.
• Pauli’s principle is essential for understanding electron configuration, chemical bonding, and the periodic table.

---

16. 🎯 Hund’s Rule of Maximum Multiplicity

🔍 What is Hund’s Rule?

Hund’s Rule of Maximum Multiplicity explains how electrons are filled into orbitals of the same energy level (called degenerate orbitals) such as p, d, or f subshells.

✅ Hund’s Rule – Statement:

“Electrons occupy all the degenerate orbitals of a subshell singly before pairing begins, and all unpaired electrons in singly occupied orbitals must have the same spin.”

🧠 Key Concepts in Simple Words

• Orbitals within the same subshell (like 2pₓ, 2pᵧ, 2p𝓏) are called degenerate – they have the same energy.
• When electrons are added to such orbitals, each orbital gets one electron first.
• Only after every orbital has one electron, do electrons start pairing.
• Also, these unpaired electrons must all have the same spin (usually ↑).

⚛️ Why Does Hund’s Rule Exist?

• Electrons are negatively charged and repel each other.
• To minimize repulsion, electrons prefer to stay in separate orbitals when possible.
• This leads to more stability and lower energy for the atom.

🔢 Example 1: Nitrogen (Z = 7)

Electron configuration: 1s² 2s² 2p³

The 2p subshell has 3 orbitals (2pₓ, 2pᵧ, 2p𝓏).
We need to place 3 electrons in them.

Correct arrangement (using Hund’s Rule):

2p orbitals:
↑   ↑   ↑

Each orbital gets one electron with parallel spin (same direction).

❌ Incorrect Arrangement (Violates Hund’s Rule):

2p orbitals:
↑↓  ↑   –

This has unnecessary pairing and empty orbitals → unstable.

🔢 Example 2: Oxygen (Z = 8)

Electron configuration: 1s² 2s² 2p⁴

Now we need to place 4 electrons in the 2p orbitals.

Correct arrangement:

2p orbitals:
↑↓  ↑   ↑

• First, 3 electrons go singly into the 3 orbitals.
• The 4th electron pairs with one of them (still follows Hund’s Rule).

🔁 Summary Table

Hund’s Rule Focus	Explanation
Degenerate Orbitals	Orbitals with same energy (e.g., 2pₓ, 2pᵧ, 2p𝓏)
Maximum Multiplicity	Maximize the number of unpaired electrons
Electron Filling Order	First fill each orbital singly, then pair
Spin of Electrons	All unpaired electrons must have the same spin

🎯 Application in Periodic Table

Hund’s Rule helps explain:

• Magnetic properties (Paramagnetic vs Diamagnetic)
• Stability of half-filled and fully filled subshells
• Shape and structure of orbital diagrams

🔄 Hund’s Rule vs Pauli Exclusion vs Aufbau Principle

Rule	What It Says
Pauli	No 2 electrons in an atom can have same 4 quantum numbers
Hund	Electrons fill degenerate orbitals singly first with same spin
Aufbau	Electrons fill orbitals in increasing order of energy

All three rules work together to determine how electrons are arranged in an atom.

📝 Practice Questions (For JEE/NEET)

🔹 MCQ:

Q: Which of the following correctly represents the electron configuration of nitrogen (Z = 7) in 2p orbitals?

(A) ↑↓ ↑ –
(B) ↑ ↑ ↑
(C) ↑↓ – –
(D) ↑↓ ↑↓

Answer: (B)

🔹 Assertion-Reason:

Assertion: Unpaired electrons in degenerate orbitals have the same spin.
Reason: This leads to lower energy due to reduced electron repulsion.

✅ Both Assertion and Reason are true.

✅ Final Summary – Quick Points

• Hund’s Rule applies to orbitals of the same energy level.
• Fill each orbital with one electron first, all with parallel spins.
• Only after that, start pairing the electrons.
• Helps to understand magnetism, reactivity, and stability of elements.

---

17. Electronic Configuration of Elements (Z ≤ 30)

📘 What is Electronic Configuration?

Electronic Configuration is the arrangement of electrons in an atom’s orbitals.

Each electron in an atom occupies an orbital in a specific order based on:

• Aufbau Principle (electrons occupy orbitals in order of increasing energy),
• Pauli’s Exclusion Principle (no two electrons can have the same 4 quantum numbers),
• Hund’s Rule (electrons occupy degenerate orbitals singly first).

🧠 Orbital Energy Order (Aufbau Sequence)

Electrons fill orbitals in this order:

CopyEdit1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p

💡 Note: Even though 3d comes after 4s in numbering, 4s is filled first because it has lower energy.

⚛️ Maximum Electrons per Subshell:

Subshell	Maximum Electrons
s	2
p	6
d	10
f	14

---

📍 Format: Electronic Configuration (Z = Atomic Number)

Let’s go from Z = 1 to 30, element by element.

🧪 Z = 1 to 10

Z	Element	Configuration
1	H	1s¹
2	He	1s²
3	Li	1s² 2s¹
4	Be	1s² 2s²
5	B	1s² 2s² 2p¹
6	C	1s² 2s² 2p²
7	N	1s² 2s² 2p³
8	O	1s² 2s² 2p⁴
9	F	1s² 2s² 2p⁵
10	Ne	1s² 2s² 2p⁶

🔹 Neon (Z=10) is a noble gas → completed 2nd shell.

🧪 Z = 11 to 18

Z	Element	Configuration
11	Na	1s² 2s² 2p⁶ 3s¹
12	Mg	1s² 2s² 2p⁶ 3s²
13	Al	1s² 2s² 2p⁶ 3s² 3p¹
14	Si	1s² 2s² 2p⁶ 3s² 3p²
15	P	1s² 2s² 2p⁶ 3s² 3p³
16	S	1s² 2s² 2p⁶ 3s² 3p⁴
17	Cl	1s² 2s² 2p⁶ 3s² 3p⁵
18	Ar	1s² 2s² 2p⁶ 3s² 3p⁶

🔹 Argon (Z=18) is a noble gas → completed 3rd shell.

🧪 Z = 19 to 30 (Includes Transition Metals)

Z	Element	Configuration
19	K	[Ar] 4s¹
20	Ca	[Ar] 4s²
21	Sc	[Ar] 3d¹ 4s²
22	Ti	[Ar] 3d² 4s²
23	V	[Ar] 3d³ 4s²
24	Cr	[Ar] 3d⁵ 4s¹ ✅ (exception)
25	Mn	[Ar] 3d⁵ 4s²
26	Fe	[Ar] 3d⁶ 4s²
27	Co	[Ar] 3d⁷ 4s²
28	Ni	[Ar] 3d⁸ 4s²
29	Cu	[Ar] 3d¹⁰ 4s¹ ✅ (exception)
30	Zn	[Ar] 3d¹⁰ 4s²

⚠️ Exceptions You MUST Remember:

Some elements do not follow the expected order due to extra stability of half-filled (d⁵) and fully-filled (d¹⁰) d-orbitals:

Element	Expected Configuration	Actual Configuration	Why?
Cr (Z=24)	[Ar] 3d⁴ 4s²	[Ar] 3d⁵ 4s¹ ✅	Half-filled d-subshell
Cu (Z=29)	[Ar] 3d⁹ 4s²	[Ar] 3d¹⁰ 4s¹ ✅	Fully-filled d-subshell

🔍 Important NEET & JEE Notes

• Know exceptions (Cr and Cu) – highly tested in exams.
• Be comfortable using noble gas shorthand notation.
• Understand how configuration affects valency, magnetism, and chemical reactivity.

🧠 Quick Memory Tip (Order of Orbitals):

Use the diagonal rule or memorize this sequence:

python-replCopyEdit1s  
2s 2p  
3s 3p  
4s 3d 4p  
5s 4d 5p  
...

➡ Fill diagonally from top to bottom.

📝 Practice Question Examples

MCQ 1:

Q: What is the electron configuration of Calcium (Z = 20)?
A) [Ne] 3s² 3p⁶ 3d²
B) [Ar] 4s²
C) [Ne] 3s² 3p⁶
D) [Ar] 3d²

✅ Answer: B

MCQ 2:

Q: Chromium shows unusual electron configuration due to:
A) Stability of half-filled p-orbitals
B) Stability of half-filled d-orbitals
C) Paired electrons are unstable
D) Hund’s rule violation

✅ Answer: B

✅ Final Summary

• Z ≤ 30 covers elements from Hydrogen to Zinc.
• Use Aufbau, Pauli, and Hund’s rules for correct configurations.
• Know and understand exceptions like Cr and Cu.
• Use noble gas notation to simplify long configurations.
• These configurations affect an element’s properties, bonding, and position in the periodic table.

---

18.🌈 Line Spectrum of Hydrogen: Lyman, Balmer, Paschen Series

🔍 What is the Line Spectrum ?

When a hydrogen atom’s electron jumps from a higher energy level (n₂) to a lower energy level (n₁), it emits energy in the form of light.
This light is not continuous — it appears as distinct lines of different colors or wavelengths. This is called the line spectrum.

These lines form specific series, each corresponding to a particular region of the electromagnetic spectrum.

⚛️ Why Does Hydrogen Show Line Spectrum?

• Hydrogen has only one electron, which can absorb or emit energy.
• When excited, the electron jumps to a higher energy level (n₂).
• It then falls back to a lower level (n₁), releasing energy as a photon (light).
• The wavelength (or frequency) of this light corresponds to a specific color or type of electromagnetic radiation.

🧪 Formula for Line Spectrum

The Rydberg formula is used to calculate the wavelength (λ) of emitted light:

1/ λ ​= R_H ​( ​1/ n²₁​−1/n²₂​​)

Where:

• λ= wavelength of emitted light
• R_H​ = Rydberg constant = 1.097 × 10⁷ m⁻¹
• n₁ = lower energy level (fixed for each series)
• n₂​ = higher energy level (n₂>n₁​)

🔢 Important Spectral Series of Hydrogen

Let’s understand the 3 major series — Lyman, Balmer, and Paschen — with their energy level transitions and regions.

1️⃣ Lyman Series

Feature	Details
n1=1n_1 = 1n1​=1	Electron falls to first shell
n2=2,3,4…n_2 = 2, 3, 4…n2​=2,3,4…	From higher shells
Region	Ultraviolet (UV)
Example Transition	2 → 1, 3 → 1, 4 → 1…

📌 Lyman series lies in the ultraviolet region, so it is invisible to human eyes.

2️⃣ Balmer Series

Feature	Details
n1=2n_1 = 2n1​=2	Electron falls to second shell
n2=3,4,5…n_2 = 3, 4, 5…n2​=3,4,5…	From higher shells
Region	Visible light
Example Transition	3 → 2, 4 → 2, 5 → 2…

📌 Balmer series is the only series visible to the human eye (shows as colored lines).

3️⃣ Paschen Series

Feature	Details
n1=3n_1 = 3n1​=3	Electron falls to third shell
n2=4,5,6…n_2 = 4, 5, 6…n2​=4,5,6…	From higher shells
Region	Infrared (IR)
Example Transition	4 → 3, 5 → 3, 6 → 3…

📌 Paschen series lies in the infrared region, so it is not visible to the human eye.

📊 Summary Table of Hydrogen Spectral Series

Series	n1n_1n1​	n2n_2n2​ values	Region of Spectrum	Visible to Eye?
Lyman	1	2, 3, 4…	Ultraviolet (UV)	❌ No
Balmer	2	3, 4, 5…	Visible	✅ Yes
Paschen	3	4, 5, 6…	Infrared (IR)	❌ No
Brackett	4	5, 6, 7…	Infrared (IR)	❌ No
Pfund	5	6, 7, 8…	Infrared (IR)	❌ No

👉 You only need to focus on Lyman, Balmer, and Paschen for Class 11 & NEET/JEE.

🧠 Key Concept: Energy Level Diagram

Here’s a simple representation of energy levels and series:

n=6 ─┬─────────────┐
     │             │
n=5 ─┼─────────────┼───> Paschen (to n=3)
     │             │
n=4 ─┼─────────────┼───> Balmer (to n=2)
     │             │
n=3 ─┼─────────────┼───> Lyman (to n=1)
     │             │
n=2 ─┼─────────────┘
     │
n=1 ─┘

• Each jump to a lower energy level emits a photon of specific energy.
• The greater the energy difference, the shorter the wavelength of the emitted photon.

🔥 Energy vs Wavelength

• Lyman series → Highest energy → Shortest wavelength (UV)
• Balmer series → Medium energy → Medium wavelength (Visible)
• Paschen series → Low energy → Longer wavelength (IR)

🧪 Real-World Applications

• Spectroscopy: Identifying hydrogen in stars and distant galaxies.
• Astrophysics: Studying the composition and temperature of celestial bodies.
• Atomic models: Basis of Bohr’s model and quantum theory.

📝 NEET / JEE Practice Questions

MCQ 1:

Q: Which transition in hydrogen gives a line in the visible region?
A) n=3 → n=1
B) n=2 → n=1
C) n=4 → n=2
D) n=5 → n=3

✅ Answer: C (Balmer series)

MCQ 2:

Q: The spectral series of hydrogen that lies in the ultraviolet region is:
A) Balmer
B) Paschen
C) Lyman
D) Brackett

✅ Answer: C

✅ Final Summary

• Hydrogen emits line spectra due to electron transitions between energy levels.
• Lyman Series: UV region (n₂ → 1)
• Balmer Series: Visible region (n₂ → 2)
• Paschen Series: IR region (n₂ → 3)
• Use the Rydberg formula to calculate wavelength.
• Important in quantum theory, astrophysics, and spectroscopy.

---

19. 🌊 Significance of Wave Function (ψ and ψ²)

🔍 What is a Wave Function (ψ) ?

In quantum mechanics, the wave function (ψ) is a mathematical expression that describes the quantum state of a particle, like an electron in an atom.

It was introduced by Erwin Schrödinger in his famous wave equation: H^ψ=Eψ\hat{H} \psi = E \psiH^ψ=Eψ

Where:

• ψ = wave function
• H^ = Hamiltonian operator (total energy)
• E = total energy of the system

⚠️ Note: ψ has no direct physical meaning, but it contains all the information about the state of the electron.

🧠 Physical Meaning Lies in ψ² (psi squared)

Although ψ itself does not have a physical meaning, its square, that is, ψ² (read as “psi squared”), is very important.

🔵 What Does ψ² Represent?

👉 ψ² gives the probability density.

In simple words:

ψ² = Probability of finding the electron in a small region of space

That means:

• Where ψ² is large, the chance of finding the electron is high.
• Where ψ² is small or zero, the chance is low or none.

✅ So, ψ² tells us where the electron is most likely to be found around the nucleus.

🎯 Example: The Hydrogen Atom

In the hydrogen atom:

• The electron is not orbiting like a planet.
• Instead, it exists as a cloud of probability.
• This cloud is shaped by the values of ψ².

This concept is the foundation of the electron cloud model.

📚 Key Terms Explained

🔸 Probability Density (ψ²)

The likelihood of finding an electron at a point in space.

🔸 Orbital

A region in space where ψ² is significant (not zero). It’s where the electron is most likely to be found.

🔄 Summary Table

Symbol	Meaning	Physical Meaning?	Unit
ψ	Wave function	❌ No direct meaning	Depends on system
ψ²	Probability density	✅ Yes (has meaning)	Probability/volume

📊 Graphical Idea

Imagine a 3D cloud around the nucleus:

• At the center (near nucleus), ψ² is highest → electron is more likely here.
• As you move away, ψ² decreases.
• At some distances, ψ² becomes zero → electron is never found there (called nodes).

⚛️ Node and ψ²

• A node is a region where ψ² = 0
• That means the electron has zero probability of being present there.

Types of nodes:

• Radial nodes (spherical)
• Angular nodes (planar or conical)

🧪 Significance in Chemistry

Why is ψ² important for chemists and physicists?

• It helps visualize atomic orbitals.
• It predicts chemical bonding and molecular shapes.
• It explains electron density and reactivity.

🧠 Real-Life Analogy

Imagine you’re playing hide-and-seek with an invisible friend in a room:

• ψ² gives you a map showing where your friend is most likely to be hiding.
• Darker regions = high chance (more probability)
• White areas = zero chance (nodes)

📝 NEET & JEE Question Examples

MCQ 1:

Q: The physical significance of ψ² is:
A) Velocity of electron
B) Momentum of electron
C) Probability of finding the electron
D) Energy of electron

✅ Answer: C

MCQ 2:

Q: At a node, the value of ψ² is:
A) Maximum
B) Minimum
C) Zero
D) Infinite

✅ Answer: C

✅ Final Summary

Term	Meaning
ψ	Mathematical function — no direct meaning
ψ²	Probability density — tells us where electron is likely to be found
Node	Point where ψ² = 0 (electron is never found)

• ψ² is the real hero in quantum mechanics — used to determine electron clouds, orbitals, and atomic structure.

---

20. 🧠 Nodes, Radial & Angular Nodes, and Nodal Planes

🔍 What is a Node?

A node is a point or region in an atomic orbital where the probability of finding an electron is zero.

In other words: ψ²= 0  at nodes

There are two main types of nodes:

1. Radial Nodes (also called spherical nodes)
2. Angular Nodes (also called nodal planes)

⚛️ Total Number of Nodes

For any orbital defined by quantum numbers: Total Nodes = n−1

Where:

• n = principal quantum number
• l = azimuthal (angular momentum) quantum number

Then:

Number of Radial Nodes = n−l−1

Number of Angular Nodes=l

📘 Example Table: Total, Radial, and Angular Nodes

Orbital	n	l	Total Nodes = n−1	Angular Nodes = l	Radial Nodes = n−l−1
1s	1	0	0	0	0
2s	2	0	1	0	1
2p	2	1	1	1	0
3s	3	0	2	0	2
3p	3	1	2	1	1
3d	3	2	2	2	0
4d	4	2	3	2	1

🔴 1. Radial Nodes (Spherical Nodes)

• Definition: A radial node is a spherical surface around the nucleus where the probability of finding the electron is zero.
• Radial nodes depend on both n and l:

Radial nodes=n−l−1

• Present in s, p, d, and f orbitals when nnn is large enough.

📌 Example:

• In the 2s orbital (n=2, l=0):
  Radial nodes=2−0−1=1

🟢 2. Angular Nodes (Nodal Planes)

• Definition: An angular node is a plane or cone-shaped region passing through the nucleus where the electron probability is zero.
• Angular nodes depend only on the azimuthal quantum number:

Angular nodes=l\text{Angular nodes} = lAngular nodes=l

Orbital Type	l	Angular Nodes (nodal planes)
s	0	0
p	1	1
d	2	2
f	3	3

🧠 What are Nodal Planes ?

• Nodal planes are a type of angular node.
• They are flat 2D planes where ψ²= 0 , i.e., electrons cannot exist.

🔸 Example:

• In a p-orbital:
  • The shape is dumbbell.
  • There is 1 nodal plane (angular node).
  • For 2pₓ, the nodal plane is the yz-plane.
• In a dₓy orbital:
  • There are 2 nodal planes: xz and yz.

🎨 Visual Summary

Orbital	Shape	Angular Nodes (Nodal Planes)
2s	Spherical	0
2pₓ	Dumbbell (along x)	yz-plane
3dₓy	Cloverleaf	xz-plane and yz-plane

📘 JEE-Level Concept Points

• Nodes are regions of zero electron density.
• Radial nodes are spherical shells, found in all orbitals depending on n−l−1.
• Angular nodes are planar or conical, determined by lll.
• Orbitals with same n but different l have different numbers of angular nodes.
• Total nodes = radial + angular nodes

📝 Practice Questions (JEE Style)

MCQ 1:

Q: The number of radial and angular nodes in a 3p orbital are:
A) 1, 1
B) 2, 0
C) 1, 2
D) 0, 3

✅ Answer: A
(3p: n = 3, l = 1 → Radial = 3 − 1 − 1 = 1; Angular = 1)

MCQ 2:

Q: The total number of nodes for a 4d orbital is:
A) 3
B) 2
C) 4
D) 5

✅ Answer: A
(4d: n = 4, l = 2 → Total nodes = 4 − 1 = 3)

✅ Final Summary

Type	Formula	Shape	Depends On
Total Nodes	n−1	–	Principal quantum number
Radial Nodes	n−l −1	Spherical	n and l
Angular Nodes	l	Planar/conical	Only l

• Nodal Planes = Angular Nodes = Plane-shaped regions of zero probability.

---

21. ⚡ Energy Level Diagrams

🔍 What is an Energy Level Diagram?

An Energy Level Diagram is a graphical representation of the energy of atomic orbitals arranged in increasing order of energy.

It shows:

• How electrons fill orbitals
• The relative energy of orbitals
• Helps understand electronic configuration

🧠 Why Do We Need Energy Level Diagrams?

Because electrons occupy the lowest energy orbitals first (as per the Aufbau Principle), we need to know the energy order of the orbitals.

But — orbitals do not always fill in numerical order (1, 2, 3…).

For example:

• The 4s orbital is filled before the 3d orbital
• This happens due to overlapping of energy levels

So, an energy level diagram helps avoid mistakes.

📘 Key Rules That Govern the Diagram

1. Aufbau Principle

Electrons fill orbitals starting from the lowest energy to the highest.

Filling Order (Based on Energy):
1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s …

2. Pauli’s Exclusion Principle

Each orbital can hold a maximum of 2 electrons, with opposite spins.

3. Hund’s Rule of Maximum Multiplicity

Electrons fill degenerate orbitals (same energy, like p, d, f) singly first before pairing.

🎯 Aufbau Order (Diagonal Rule Method)

You can remember the energy filling sequence using the Diagonal Rule.

🔻 How It Works:

Like This-   1s
               ↓
             2s → 2p
               ↓     ↓
             3s → 3p → 4s
               ↓     ↓     ↓
             3d → 4p → 5s → 4d
               ↓     ↓     ↓     ↓
             5p → 6s → 4f → 5d → 6p
               ↓     ↓     ↓     ↓     ↓
             7s → 5f → 6d → 7p

Just follow the arrows diagonally downward to get the filling order.

🔋 Energy Level Diagram (Up to Z = 30)

Orbitals (With Their Electron Capacities)

Orbital	Max Electrons
1s	2
2s	2
2p	6
3s	2
3p	6
4s	2
3d	10
4p	6

Up to atomic number 30 (Z = 30), orbitals fill as:

→ 1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p

📊 Energy Level Diagram (Visual Representation)

Like This-   1s 
↑↓           2s
↑↓ ↑↓ ↑↓     2p
↑↓           3s
↑↓ ↑↓ ↑↓     3p
↑↓           4s
↑↓ ↑↓ ↑↓ ↑↓ ↑↓    3d
↑↓ ↑↓ ↑↓         4p

• Each arrow ↑ or ↓ represents one electron with spin.
• Orbitals of same type (p, d, f) have multiple sub-levels (3 for p, 5 for d).

🧪 Energy Comparison Between Orbitals

Orbital	Relative Energy
1s	Lowest
2s	↑
2p	↑
3s	↑
3p	↑
4s	↑
3d	↑
4p	↑ (Highest among these)

Note: Even though 3d has n = 3, it is higher in energy than 4s. That’s why 4s fills before 3d.

🧠 Key Concepts for JEE/NEET

• Orbitals are filled based on increasing energy, not order of n.
• Use (n + l) rule to compare orbital energies.

🔸 (n + l) Rule

• Lower n+ln + ln+l = lower energy
• If same n+ln + ln+l, then lower n = lower energy

Orbital	n	l	n + l
4s	4	0	4
3d	3	2	5

→ 4s is filled before 3d

📝 JEE/NEET Question Examples

MCQ 1:

Q: Which orbital is filled just after 3p?
A) 4p
B) 3d
C) 4s
D) 5s

✅ Answer: C (4s)

MCQ 2:

Q: Which of the following orbitals has the highest energy among these?
A) 3s
B) 3p
C) 4s
D) 3d

✅ Answer: D (3d)

MCQ 3:

Q: Which of the following will be filled first?
A) 4s
B) 3d

✅ Answer: A (4s)
(Use the (n + l) rule: 4s = 4, 3d = 5)

🔚 Final Summary

Concept	Rule/Explanation
Aufbau Principle	Fill orbitals from lower to higher energy
Pauli’s Principle	Max 2 electrons per orbital with opposite spins
Hund’s Rule	Degenerate orbitals fill singly first, then pair
(n + l) Rule	Lower (n + l) = lower energy
Filling Order	1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p (for Z ≤ 30)

---

For Important Questions & Answer, Message On Instagram→ Learn Sufficient Notes

🥰Learn Sufficient Notes🥰