General Introduction-

  • The word atom come from Greek word ‘a-tomio‘ which means ‘non-divisible‘.
  • The first atomic theory was proposed by a British school teacher, John Dalton (1766-1844) in 1808.
  • The atom made of sub-atomic particles i.e electron, proton and neutron. Today, there are 32 sub atomic particles were discovered but only electron, proton and neutron are consider as fundamental particles.

DISCOVERY OF SUB ATOMIC PARTICLES-

Like charge repel with each other whereas unlike charge attract with each other.

ELECTRON-

  • Discovery of Electron-
    • In 1850s, many scientist mainly Faraday begin to study on cathode ray discharge tube.
    • Cathode ray discharge tube-
      • It is electrically discharge in partially evacuated tube.
      • It is made from glass and contain 2 electrode (conductor which allow to pass electricity, heat etc.) on the end of both side which sealed on it.
      • The cathode ray travel in straight line and cathode ray can deviate form electrical and magnetic field.
      • Cathode ray is composed form very small negatively charged particles called electrons. It is proved by JJ Thomson in (1897) by an experiment of cathode ray discharge tube.
      • So JJ Thomson was discovered electron in 1897 by perform an experiment of cathode ray tube.
      • Experiment- When he make holes on anode and do coating behind anode of phosphorescent material zinc sulphide and pass very high voltage current(about 10,000 volts) in cathode ray tube on very low pressure, then current start to flowing form negative electrode (cathode) to positive electrode (anode). These rays called cathode rays. Then there rays passing through anode, strike the zinc sulphide coating, he noticed that the bright spot (green color) developed on coating.
      • characteristic of cathode rays-
        • Cathode rays start form cathode and move toward to anode.
        • These rays are not visible but they can observe by brightness.
        • Also in Television, cathode ray tube used to show picture with this material.
        • Cathode ray do not depend on material of electrode and nature of gas which present in cathode ray tube.
  • Charge of Electron-
    • R.A. Millikan(1868-1953) determine the charge of electron form Oil Drop Experiment which also conduct by he.
    • The Millikan oil drop experiment measured the charge of an electron. Tiny oil droplets were suspended in an electric field. By adjusting the field’s strength, Millikan calculated the charge on the droplets, revealing that the charge was always a multiple of a fundamental value, which he determined to be the charge of a single electron.
    • The charge of electron is 1.6 * 10-19 Coulomb(C).
  • Ratio of charge and mass of electron(me) are-
    • In 1897, British physicist J.J. Thomson measure the charge to mass ratio of electron by using cathode ray tube and applying electron electrical and magnetic field perpendicular to each other as well as to the path of eletrons.
    • e/me = 1.758820 * 1011 C Kg-1
    • Since the electron is negatively charged.
    • Discovery of Proton-
      • Proton was discovered by Ernest Rutherford in 1917.
      • Discovery of canal rays which carrying positively charged particle.
    • Characteristic of anode rays-
      • Anode rays start form anode and move toward to cathode.
      • These rays are not visible but they can observe by brightness.
      • Move in straight lines.
      • Mass depends on the gas used.
      • Deflected by electric and magnetic fields.
      • Produce mechanical effects (e.g., turn a paddle wheel).
      • The smallest and positively charged ion was obtain from hydrogen are called proton.
  • Discovery of Neutron-
    • Neutron were discovered by James Chadwick in 1932.
    • These particles was discovered by bombarding by α-particle(Helium) on a thin sheet of Beryllium(Be).
    • Neutron are neutral in charge.
  • The Atomic mass unit is also called unified mass(u)
  • The name, charge, symbol, relative charge, Mass/kg, Mass/u, approx. mass/u are in table-
NameSymbol Charge Relative ChargeMass Mass / uApprox. mass /u
Electrone-1.6*10-19C-19.12*10-31Kg0.000540
Protonp+1.6*10-19C+11.672*10-27Kg1.007271
NeutronN001.674*10-27Kg1.008671

Atomic Models-

  • Thomson Model of Atom)-
    • This model also known as the plum pudding model, Watermelon model and it was proposed by J.J. Thomson in 1904.
    • Thomson was awarded Nobel price for physics in1906 for his work.
    • He suggested that-
      • Atoms are spheres of positive charge distributed uniformly.
      • Negatively charged electrons are uniformly embedded like “plums” in the “pudding” of positive charge.
      • This model explained the overall neutrality of atoms (equal positive and negative charges).
      • The radium of atom is approx. 10-10 meter.
    • Limitation or drawback of this model is-
      • No nucleus in the model.
      • Could not explain Rutherford’s gold foil experiment.
      • Did not describe electron arrangement.
  • Nuclear Model of Atom by Rutherford-
    • Rutherford and his 2 students(Hans Geiger and Ernest Marsden) bombarded very thin gold foil with α-particle(Helium) scattering experiment.
    • He directed the high energy stream of α-particle from radioactive source on sheat of gold foil (about 100 nm thickness)
    • His observation is-
      • Most of the α-particle are directly passed through from gold foil.
      • A small amount of α-particle was deflected by small angle and some large angle.
      • A very few(about 1 from 20,000) bounced back at 180°.
    • His conclusion is-
      • Atoms have a small, dense, positively charged area in center called nucleus.
      • Negatively charged electrons are orbit around the nucleus.
      • Most of the space in atom is empty and most of the mass atom present in nucleus.
    • His model is-
      • Most of the mass of atom present in positive charge dense concentrated extremly small region which he called nucleus.
      • The electron move around the nucleus with very high speed in circular path called orbits just like in solar system that all planets revolve around the sun on own axis.
      • Nucleus and electrons are held together by electrostatic force of attraction.

Some Important Concepts-

  • Mass Number-
    • Mass number is the total number of protons and neutrons in an atom’s nucleus.
    • It help to determine mass of atom.
    • Mass number = Protons(Z) + Neutrons(n).
    • It is represented by A.
      • mass =
  • Atomic Number-
    • Atomic number is the number of protons in an atom’s nucleus.
    • It determines the element’s identity and its position in the periodic table.
    • It also equals the number of electrons in a neutral atom.
    • It is represented by Z.
      • Atomic number(Z) = number of proton in nucleus = number of electron in neutral atom
  • Isotopes-
    • They are the atom with same atomic number but different mass numbers. ex- Carbon-12 and Carbon-14 (both are isotopes of carbon).
  • Isobars-
    • They are the atom with same mass number but different atomic number.
  • Isotone-
    • They are the atoms of different elements that have the same number of neutrons but different numbers of protons.
  • Isoelectronic Species-
    • They are atoms, ions, or molecules that have the same number of electrons. ex- Na+ (11 protons, 10 electrons) and F– (9 protons, 10 electrons).

Development of Bohr model of atom-

Varaition of heat capacity of solid as fuction of temperature.

Dual nature of electromagnetic radiations– wave and particle nature (Planck ‘s Quantum Theory).

That means the electromagnetic radiation shows both wave nature and particle nature. We will study both deeply.

Wave Nature of Electromagnetic Radiation-

In mid-19th century, many physisicts study on absorption and emission of radiation by heasted object, called thermal radiation. They were try to find what indeed the thermal radiation.

The first active study of thermal radiation laws occured in 1850’s and the theory of electromagnetic waves and emission of such waves by accelerating charged particles was developed by James Clerk Maxwell in 1870’s, and it was experimentally proved by Heinrich Hertz later.

The first Maxwell explanation in 1870 about interaction between the charged body and and macroscopic level. He say that when electrically charged particles move under acceleration, thent he alternating electrical and magnetical field are produced and transmitted. The field are transmitted in the form of wave, called electromagnetic waves or electromagnetic radiation.

Maxwell again suggested that light waves are associated with oscilating electric and magnetic character.

The simple properties of electromagnetic wave motion are-

  • Oscillating charge particle produced the oscillating electric and magnetic field which are perpendicular to each other and direction.
  • They can aslo move vaccum, because they does nt requided any medium to propagate.
  • There are many different types of electrmagnetic radiations which differ in wavelength. It make eectromagnetic spectrum which are different names in different regions.

The visible light comes in small region around 1015Hz.

The radiations are characterised by frequency(f or ν) and wavelength(λ)-

Frequency means the number of waves whuch pass from a given point in 1 second.The SI unit of frequency is hertz(Hz or s-1).

The wavelength is a lenght of complete wave. The SI unit of wavelength is meter(m).

The electromagnetic readiation have different wavelength and frequencies.

In vaccum all types of electromagnetic waves travel at same speed is 3 * 108ms-1. This number is also called speed of light which is denoted by c.

The wavenuber is the number of wavelength as per unit length. It is reciprocal to wavelength. Its unit is m-1 or cm-1.

The relation between wavelength(λ), speed of light(c), frequency(v)-

λ = c / v

wavenumber = 1 / wavelenght

frequency = 1 / time period

The Particle Nature of electromagentic radiation- Planck ‘s Quantum Theory.

1. Wave and Particle Nature of Light:

  • Some experiments like diffraction and interference show that light behaves as a wave.
  • However, some phenomena couldn’t be explained by wave theory:
    • Black-body radiation: The way hot objects emit radiation.
    • Photoelectric effect: When light strikes a metal surface, it ejects electrons.
    • Heat capacity of solids: How heat capacity changes with temperature.
    • Atomic line spectra: Specific lines in the spectrum of light emitted by atoms, especially hydrogen.

2. Black-Body Radiation:

  • A black body absorbs and emits all wavelengths of light perfectly. It is in thermal equilibrium, radiating as much energy as it absorbs.
  • When the temperature of a black body increases:
    • The intensity of emitted radiation increases.
    • The wavelength of maximum radiation shortens (shifts toward blue).
  • The intensity of radiation from hot bodies varies with temperature and wavelength.
  • Classical physics couldn’t explain this, but Max Planck proposed that energy is emitted in discrete quantities (quanta). These quantities are related to frequency by the equation E = hν, where E is energy, h is Planck’s constant (6.626 × 10⁻³⁴ J·s), and ν is frequency.

3. Photoelectric Effect:

  • In 1887, H. Hertz discovered that light striking certain metals ejected electrons. This phenomenon is called the photoelectric effect.
  • Key observations:
    1. Electrons are ejected as soon as the light strikes the metal, without any delay.
    2. The number of ejected electrons depends on light intensity.
    3. There is a minimum frequency (threshold frequency, ν₀) of light below which no electrons are ejected, and above this frequency, the electrons gain kinetic energy. The kinetic energy increases with the light frequency.
  • Classical physics couldn’t explain this. According to classical theory, light’s energy should depend on intensity, but experiments showed that the kinetic energy of ejected electrons depended on frequency, not intensity.

4. Explanation by Planck and Einstein:

  • Planck proposed that energy is quantized (discrete amounts), leading to the quantum theory of radiation.
  • Einstein explained the photoelectric effect using Planck’s theory. He suggested that light consists of particles (photons) and that energy is transferred in packets. The minimum energy required to eject an electron is called the work function (W₀). The excess energy (hν – hν₀) is transferred as the kinetic energy of the ejected electron.

Key Concepts:

  • Quantization of energy: Energy can only exist in discrete quantities.
  • Planck’s constant (h): A fundamental constant in quantum mechanics.
  • Threshold frequency (ν₀): The minimum frequency required to eject electrons from a metal.
  • Work function (W₀): The energy needed to remove an electron from a metal surface.

Dual Behaviour of Electromagnetic Radiation

  • Dilemma in Understanding Light: The nature of light was confusing for scientists because it could explain some phenomena (black body radiation, photoelectric effect) through its particle nature but did not fit the wave-like behavior (interference, diffraction) of light.
  • Resolution: To solve this issue, scientists proposed that light behaves both as a particle and a wave—this is known as dual behaviour. Depending on the situation, light can either show wave-like properties or particle-like properties. When light interacts with matter, it acts like particles (photons), but when it travels, it behaves like a wave (interference and diffraction).
  • Particle Nature: A photon, a particle of light, has energy proportional to its frequency (E = hν). When photons hit a metal’s surface, they can transfer their energy to electrons, ejecting them from the metal.
  • Energy Transfer and Kinetic Energy: The energy transferred to the ejected electron depends on the photon’s energy. The more energy the photon has, the higher the kinetic energy of the ejected electron. This shows that the kinetic energy of an ejected electron is linked to the frequency of the light.
  • Einstein’s Contribution: Albert Einstein explained this phenomenon in 1905 and won the Nobel Prize in 1921 for his work on the photoelectric effect. His research established that light has both particle and wave properties, which laid the groundwork for quantum mechanics.
  • Photons and Frequency: The energy of a photon is directly related to its frequency, with the equation E = hν, where h is Planck’s constant. The higher the frequency, the higher the photon energy.
  • Problem-Solving in Physics: Example problems show how to calculate photon energy and the energy of a mole of photons. These calculations involve using Planck’s constant and the frequency of light.
  • Photoelectric Effect: When light of sufficient frequency hits a metal, electrons are ejected. The frequency of the light must be above a certain threshold for the photoelectric effect to occur, and the kinetic energy of the emitted electrons is linked to the light’s frequency.

Atomic Spectra and Emission/Absorption Spectra

  • Nature of Light: Light travels through various media, bending or refracting as it passes from one medium to another. When white light passes through a prism, it splits into a spectrum of colors (continuous spectrum), where violet bends the most and red bends the least.
  • Emission Spectrum: When atoms or molecules absorb energy, they get excited. Upon returning to a stable state, they emit energy as light, creating an emission spectrum. This spectrum shows bright lines at specific wavelengths, which is characteristic of the element and helps in identifying unknown substances.
  • Absorption Spectrum: An absorption spectrum is the opposite of an emission spectrum. It shows dark lines or bands where certain wavelengths of light are absorbed by the sample. These dark lines correspond to the wavelengths of light the atoms or molecules in the sample absorb.
  • Spectroscopy: The study of emission and absorption spectra is known as spectroscopy, which helps identify elements. Each element has a unique line spectrum, like a fingerprint, which can be used for chemical analysis.
  • Example: The emission spectra of gases, like sodium or hydrogen, show distinct lines corresponding to specific energy transitions within the atoms. This can help in identifying the element present, much like using fingerprints to identify a person.
  • Discovery of Elements: Spectroscopic analysis led to the discovery of new elements like rubidium, caesium, and helium. For example, helium was first discovered in the Sun’s spectrum before being found on Earth.

Line Spectrum of Hydrogen

  1. Electric Discharge in Hydrogen Gas:
    • When an electric discharge passes through gaseous hydrogen, the hydrogen molecules dissociate, and the excited hydrogen atoms emit electromagnetic radiation.
    • This radiation is in the form of discrete frequencies, leading to the creation of a line spectrum.
  2. Balmer Series:
    • In 1885, Balmer showed that the visible lines of hydrogen’s spectrum follow a formula based on wavenumber (𝜈) for values of n ≥ 3 (where n = 3, 4, 5, …).
    • The visible spectrum of hydrogen consists of lines described by the Balmer series, which is the only part of the hydrogen spectrum visible to the human eye.
  3. Rydberg’s Formula:
    • Johannes Rydberg derived a general formula to describe all spectral lines of hydrogen:
      • 1/ λ ​=RH​ / (1/n12​ -1/​n22​)
    • Here, n1​ and n2​ are integers, and the constant RH​ is the Rydberg constant (109,677 cm⁻¹).
  4. Spectral Series:
    • The first five series of spectral lines are named: Lyman (UV), Balmer (Visible), Paschen, Brackett, and Pfund (Infrared).
    • As we move from Lyman to Pfund series, the energy of the emitted radiation decreases, and the wavelengths increase (from UV to IR).
  5. Hydrogen’s Line Spectrum:
    • Hydrogen has the simplest line spectrum, consisting of discrete lines, unlike heavier atoms which have more complex spectra.
    • Common properties of line spectra:
      • Each element’s spectrum is unique.
      • There is regularity in the line spectra of elements, related to their electronic structure.
  6. Bohr’s Model of the Hydrogen Atom (1913):
    • Bohr used Planck’s concept of energy quantization to explain hydrogen’s spectrum and atomic structure.
    • Postulates:
      • Electrons move in circular orbits with fixed radii and energy around the nucleus.
      • Energy is emitted or absorbed when electrons jump between these orbits.
      • The electron’s angular momentum is quantized:
        • L= mevr = nh/2π, where n is an integer.
      • Radiation emitted or absorbed is related to the energy difference between two stationary states.
  7. Quantization of Angular Momentum:
    • Angular momentum is quantized, meaning electrons can only occupy orbits where their angular momentum is an integral multiple of h/2π.
    • This explains why only certain orbits are allowed, and why the electron does not emit radiation in a continuous manner.
  8. Bohr’s Energy Formula:
    • The energy of an electron in the nth orbit is given by:
      • En​=−2.18×10−18​/n2 J
    • As n increases, the electron’s energy becomes less negative, and the electron moves further from the nucleus.
  9. Energy and Radius:
    • The radius of the nth orbit is given by:
      • rn​ = n2a0​(where a0​=52.9pm)
    • The energy levels are negative, indicating the electron is bound to the nucleus. The most stable orbit (ground state) corresponds to n=1.
  10. Ionization:
    • When an electron is ionized (removes from the atom), its energy is zero at n=∞.
    • For n=1, the energy is at its lowest (-2.18 × 10⁻¹⁸ J).
  11. Bohr’s Model for Hydrogen-like Ions:
    • Bohr’s model also applies to ions with a single electron, such as He⁺, Li²⁺, Be³⁺, etc.
    • The energy of these ions is given by:
      • En​=−2.18×10−18​ Z2 / n2 J
    • The radius is given by:
      • rn​ = 52.9/Z ​× n2/Z
    • As the atomic number Z increases, the electron becomes more tightly bound to the nucleus.
  12. Line Spectrum Explanation:
    • The energy difference ΔE\Delta EΔE between two orbits gives the energy of the photon emitted or absorbed during a transition:
      • ΔE = Ef​ − Ei​
    • This energy is related to the frequency of radiation by E=hν, where h is Planck’s constant and ν is the frequency.
  13. Limitations of Bohr’s Model:
    • Bohr’s model failed to explain:
      • The fine details of the hydrogen spectrum (e.g., doublets).
      • The spectra of multi-electron atoms.
      • The splitting of spectral lines in magnetic (Zeeman effect) or electric fields (Stark effect).
      • The formation of chemical bonds in molecules.
    • These limitations led to the development of more advanced quantum mechanical models.

Conclusion:
Bohr’s model, despite its limitations, was a major step in understanding atomic structure and the hydrogen atom’s spectrum. However, further developments in quantum mechanics are needed for a complete explanation of atomic behavior, especially for atoms more complex than hydrogen.

1. Bohr’s Model Shortcomings:

  • The Bohr model had limitations, leading to the development of a more general model for atoms.

2. Two Key Developments:

  • Dual Behaviour of Matter: This concept, proposed by de Broglie, suggests that matter behaves both as particles and waves.
  • Heisenberg Uncertainty Principle: Proposed by Heisenberg, it states that it’s impossible to determine both the exact position and exact momentum of an electron simultaneously.

Dual Behaviour of Matter:

  • De Broglie’s Hypothesis (1924):
    • He proposed that just as light (photons) has both momentum and wavelength, electrons should also have both.
    • Relation: λ = h / mv ​where:
      • λ= wavelength
      • h= Planck’s constant (6.626×10−34Js)
      • m= mass of particle
      • v= velocity of the particle
      • Units: h in Js, mmm in kg, and v in m/s.
  • Experimental Verification:
    • De Broglie’s prediction was confirmed when it was observed that electron beams could undergo diffraction (a wave characteristic), which led to the development of the electron microscope.
  • Electrons vs. Ordinary Objects:
    • While electrons and subatomic particles have detectable wavelengths due to their small mass, ordinary objects have extremely short wavelengths that are practically undetectable.

Example Problem:

  • A problem is provided to calculate the wavelength of an electron based on its kinetic energy.

Heisenberg’s Uncertainty Principle:

  • Heisenberg’s Principle (1927):
    • It is impossible to simultaneously know the exact position (xxx) and momentum (ppp) of a particle.
    • Mathematically: Δx ⋅ Δp ≥ h/4π
      • Δx = uncertainty in position
      • Δp= uncertainty in momentum
    • If position is measured precisely, momentum becomes uncertain, and vice versa.
  • Explanation with an Analogy:
    • Trying to measure the thickness of paper with an unmarked meterstick demonstrates the idea of uncertainty in measurements.
    • Similarly, measuring the position of an electron accurately with light (photons) alters its velocity due to the high momentum of the photons.
  • Significance:
    • This principle implies that subatomic particles like electrons don’t follow fixed paths (trajectories), unlike larger objects where position and velocity determine their trajectory.
    • The uncertainty principle is more important for microscopic particles like electrons, where the uncertainties are larger. For macroscopic objects, the uncertainty is negligible.

Example Problem:

  • Applying the uncertainty principle to large objects, like a 1 mg mass, shows that the uncertainty in velocity and position is extremely small and has no practical effect.
  • Conclusion:
    • The uncertainty principle shows that the classical idea of electrons moving in fixed orbits is incorrect. Instead, their behavior is described by probabilities, not fixed positions and momentum.

Key Points for Understanding and Competitive Exams:

  1. Dual Nature of Matter: Electrons behave as both particles and waves. Their wavelength can be calculated using de Broglie’s equation.
  2. Heisenberg Uncertainty Principle: It is impossible to know both the exact position and momentum of an electron at the same time, fundamentally changing the way we view atomic structure.
  3. Electron Microscope: Uses the wave nature of electrons for high magnification (up to 15 million times).
  4. Probabilistic Model: The position and velocity of electrons cannot be precisely determined, so quantum mechanics uses probability to describe their behavior.

Reasons for the Failure of the Bohr Model:

  1. Electron Behavior: In the Bohr model, electrons were considered as charged particles orbiting the nucleus in fixed, well-defined circular paths. However, the model didn’t account for the wave nature of electrons.
  2. Heisenberg’s Uncertainty Principle: The Bohr model assumed that both the position and velocity of an electron could be known precisely at the same time. This contradicts the Heisenberg uncertainty principle, which states that it’s impossible to know both with perfect accuracy simultaneously.
  3. Dual Nature of Matter: The Bohr model ignored the wave-particle duality of matter, a fundamental concept in quantum mechanics.

Quantum Mechanical Model of the Atom:

  1. Classical vs Quantum Mechanics: Classical mechanics works well for macroscopic objects (e.g., falling stones, planets) but fails for microscopic objects (e.g., electrons). This failure is due to the classical model ignoring the dual nature of particles and the uncertainty principle. Quantum mechanics addresses this by considering both wave and particle properties of matter.
  2. Development of Quantum Mechanics: In 1926, Werner Heisenberg and Erwin Schrödinger developed quantum mechanics. Schrödinger’s equation describes the wave nature of particles and won him a Nobel Prize in 1933. The equation gives the energy levels of electrons in atoms, considering both the wave and particle nature of matter.
  3. Schrödinger’s Equation: For atoms, Schrödinger’s equation calculates the electron’s energy levels and wave functions. It incorporates the kinetic and potential energies of particles (electrons, nuclei) and gives quantized energy states. However, for multi-electron atoms, the equation cannot be solved exactly, so approximate methods are used.
  4. Wave Function and Probability: The wave function, symbolized by ψ, describes the state of an electron in an atom. The probability of finding an electron at a given location is proportional to the square of the wave function, |ψ|². This results in a “probability density,” showing where an electron is likely to be found.
  5. Quantum Numbers: Each electron is described by a set of quantum numbers that determine its energy, shape, and orientation in the atom. The three main quantum numbers are:
    • Principal Quantum Number (n): Determines the energy and size of an orbital.
    • Azimuthal Quantum Number (l): Determines the shape of the orbital.
    • Magnetic Quantum Number (ml): Describes the orientation of the orbital in space.
  6. Multi-electron Atoms: For multi-electron atoms, orbitals’ energies depend on both n and l. The Schrödinger equation for these atoms is more complex and requires approximate methods for calculation. Orbitals in these atoms are contracted compared to hydrogen-like atoms.
  7. Electron Spin: In 1925, George Uhlenbeck and Samuel Goudsmit introduced the electron spin quantum number (ms), which describes the electron’s intrinsic angular momentum. Electrons can spin in two directions: +½ or -½. This concept explains the fine structure of spectral lines and the fact that an orbital can hold at most two electrons with opposite spins.

Important Features of the Quantum Mechanical Model:

  1. Quantized Energy Levels: Electrons can only occupy specific energy levels, which arise due to their wave-like properties.
  2. Uncertainty Principle: It’s impossible to know both the exact position and velocity of an electron at the same time.
  3. Orbitals: Electrons are described by orbitals, each with a wave function. Orbitals are categorized by quantum numbers and represent regions where electrons are likely to be found.
  4. Probability Density: The probability of finding an electron in a certain region is given by |ψ|².
  5. Electron Configuration: Electrons fill orbitals in a specific order, with lower energy orbitals filling first. In multi-electron atoms, electron configuration is affected by electron-electron interactions.

Quantum Numbers and Orbitals:

  1. Principal Quantum Number (n): Defines the energy level and size of the orbital. Higher values of n correspond to orbitals farther from the nucleus.
  2. Azimuthal Quantum Number (l): Defines the shape of the orbital. Possible values depend on n.
    • l = 0 corresponds to an s orbital, l = 1 to a p orbital, l = 2 to a d orbital, etc.
  3. Magnetic Quantum Number (ml): Describes the orientation of the orbital. For each value of l, there are 2l + 1 possible values for ml.
  4. Electron Spin Quantum Number (ms): Describes the electron’s spin. It can be +½ (spin up) or -½ (spin down).

Bohr Orbit vs Atomic Orbitals:

  • Bohr Orbits: These were fixed circular paths proposed by Bohr for electron motion, which are not physically meaningful in quantum mechanics.
  • Atomic Orbitals: These are described by wave functions and have real physical significance. They represent the probability distribution for finding an electron in a specific region of space.

Summary:

  • The Bohr model failed because it did not consider the wave nature of electrons and violated the Heisenberg uncertainty principle.
  • Quantum mechanics, developed by Schrödinger, incorporates wave-particle duality and the uncertainty principle to describe the behavior of electrons in atoms.
  • The quantum mechanical model uses quantum numbers to describe the energy, shape, orientation, and spin of electrons in atoms.
  • Schrödinger’s equation explains the quantization of energy and electron probabilities in atoms.

Shapes of Atomic Orbitals

  1. Orbital Wave Function (ψ):
    • The orbital wave function (ψ) describes the electron’s position but does not directly represent a physical object. It is a mathematical function of the electron’s coordinates in space.
  2. Shape Representation:
    • The shape of an orbital is represented using boundary surface diagrams. These diagrams are used to show regions where the probability of finding an electron is high (about 90%). For example, for 1s and 2s orbitals, these shapes are spherical.
  3. S-Orbitals (spherical):
    • The 1s and 2s orbitals are spherical in shape, meaning the probability of finding the electron is the same in all directions. As the principal quantum number (n) increases, the size of the orbital increases (4s > 3s > 2s > 1s), and the electron is found further from the nucleus.
  4. P-Orbitals (lobes):
    • The 2p orbitals are not spherical; they have a shape with two lobes on either side of a plane passing through the nucleus. These lobes are oriented along the x, y, and z axes (labeled 2px, 2py, 2pz). The p orbitals also increase in size with increasing principal quantum number (4p > 3p > 2p).
    • The probability density is zero on the plane where the lobes meet.
  5. D-Orbitals (clover-shaped):
    • D orbitals begin from n = 3. There are five types: dxy, dyz, dxz, dx²–y², and dz². Most of these have similar shapes, while dz² is different. All 3d orbitals are equivalent in energy.
    • These orbitals also have angular nodes, where the probability density is zero. For example, the dxy orbital has two nodal planes passing through the origin.
  6. Node Concept:
    • Nodes are points or regions where the probability of finding an electron is zero. Radial nodes occur as the electron moves farther from the nucleus, while angular nodes relate to the orientation of the orbital.
    • For p orbitals, there is 1 angular node; for d orbitals, 2 angular nodes; and for f orbitals, 3 angular nodes.
    • The total number of nodes is given by (n-1), where n is the principal quantum number.
  7. Orbital Energy:
    • For a hydrogen atom, the energy depends only on the principal quantum number (n). The energy increases in the order: 1s < 2s = 2p < 3s = 3p = 3d < 4s = 4p = 4d = 4f.
    • For multi-electron atoms, the energy also depends on the azimuthal quantum number (l), with the order of energy being s < p < d < f within a given shell. For example, 4s has lower energy than 3d in multi-electron atoms.
  8. Effective Nuclear Charge (Zeff):
    • In multi-electron atoms, electrons experience both attraction from the nucleus and repulsion from other electrons. Electrons in inner shells shield outer electrons from the full charge of the nucleus, reducing the effective nuclear charge (Zeff) felt by outer electrons.
    • As the nuclear charge increases, the attraction between the electron and the nucleus strengthens, lowering the orbital energy (making it more negative).
  9. Shielding and Energy Order:
    • Electrons in s orbitals shield outer electrons more effectively than electrons in p or d orbitals. This affects the binding energy of electrons, with s electrons being more tightly bound than p, and p more tightly bound than d.
    • Energy within a shell decreases as the value of (n + l) decreases. If two orbitals have the same (n + l), the orbital with the smaller n value will have lower energy.
  10. Energy Order in Multi-electron Atoms:
    • In multi-electron atoms, energy levels of orbitals in the same shell differ, as seen with 4s < 3d, 6s < 5d, etc.
    • The energy of orbitals within the same subshell (like 2s, 3s, 4s, etc.) decreases as the atomic number (Z) increases due to a stronger nuclear charge.

1. Filling of Orbitals in Atoms

  • Principles Involved:
    • Aufbau Principle: Electrons fill orbitals in order of increasing energy. Lower energy orbitals are filled first before higher energy ones. The energy of an orbital depends on its nuclear charge (how strongly the nucleus pulls on the electrons).
    • Pauli Exclusion Principle: No two electrons in an atom can have the same set of four quantum numbers. In simpler terms, two electrons can share an orbital but must have opposite spins (↑ and ↓).
    • Hund’s Rule of Maximum Multiplicity: When filling orbitals of the same energy (degenerate orbitals), electrons will first fill each orbital singly with parallel spins (↑) before pairing up.

2. Order of Orbital Filling (Aufbau Sequence)

  • The sequence in which orbitals fill based on their energy levels:
    • The typical order is: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 4f, 5d, 6p, 7s.
    • This sequence may change in certain cases due to the closeness in energy between orbitals (e.g., 4s fills before 3d).

3. Pauli Exclusion Principle

  • This principle limits the number of electrons in an orbital:
    • Each orbital can hold a maximum of two electrons, and they must have opposite spins.
    • The formula for the maximum number of electrons in a shell is: 2n² (where n is the principal quantum number).

4. Hund’s Rule of Maximum Multiplicity

  • When electrons fill orbitals of the same energy (like the p, d, or f orbitals), they will first fill each orbital with one electron, having parallel spins (↑), before pairing up.
  • Half-filled and fully-filled orbitals (e.g., 3p³ or 3d⁵) are especially stable due to their symmetrical arrangement.

5. Electronic Configuration

  • The distribution of electrons into orbitals is called electronic configuration.
  • There are two common ways to represent it:
    • Shorthand notation: e.g., 1s² 2s² 2p⁶ for Neon.
    • Orbital diagram: Boxes for orbitals and arrows for electron spins.
  • Valence electrons are the electrons in the outermost shell, and core electrons are those in filled inner shells.

6. Examples of Electronic Configurations:

  • Hydrogen (H): 1s¹ (one electron in the 1s orbital).
  • Helium (He): 1s² (two electrons in the 1s orbital).
  • Lithium (Li): 1s² 2s¹ (one electron in the 2s orbital).
  • Sodium (Na): 1s² 2s² 2p⁶ 3s¹ (in shorthand: [Ne] 3s¹).
  • Chlorine (Cl): 1s² 2s² 2p⁶ 3s² 3p⁵ (in shorthand: [Ne] 3s² 3p⁵).

7. Stability of Half-Filled and Fully Filled Orbitals

  • Symmetry: Orbitals that are completely filled or half-filled (like 3d⁵ or 4s²) are more stable due to their symmetrical electron distribution.
  • Exchange Energy: In degenerate orbitals (like p, d, or f), when electrons have the same spin (↑), they can exchange places, which releases energy and increases stability.

8. Exceptions to the Rules

  • Some elements, like chromium (Cr) and copper (Cu), have exceptions in their electronic configurations.
    • Chromium: Instead of 3d⁴ 4s², it has 3d⁵ 4s¹.
    • Copper: Instead of 3d⁹ 4s², it has 3d¹⁰ 4s¹.
    • These exceptions happen because half-filled or fully filled d-orbitals (like 3d⁵ or 3d¹⁰) provide extra stability.

9. Significance of Electronic Configuration

  • The electronic configuration of atoms determines their chemical behavior. For example:
    • Why atoms combine: Atoms bond to achieve a stable electronic configuration, often resembling the nearest noble gas (like Neon or Argon).
    • Metals vs Non-metals: Metals tend to lose electrons (often having fewer valence electrons), while non-metals tend to gain electrons.
    • Reactivity: Elements like helium and argon are chemically stable and non-reactive, while halogens (like chlorine) are very reactive because they need one electron to complete their outer shell.

This chapter means-

Atoms and Atomic Models

  • Atoms are the basic building blocks of elements and are the smallest units that react chemically.
  • John Dalton’s Atomic Theory (1808) said atoms were indivisible particles, but later discoveries showed atoms are divisible and made up of three particles: electrons, protons, and neutrons.

Early Atomic Models

  1. Thomson Model (1898): Proposed that atoms were made of a positively charged “pudding” with electrons scattered inside.
    • This was later proved wrong.
  2. Rutherford Model (1909): Discovered, through an experiment with alpha particles, that an atom has a tiny, dense, positively charged nucleus at its center with electrons orbiting it.
    • This model improved on Thomson’s, but it couldn’t explain why the electrons don’t fall into the nucleus. Also, it didn’t describe how electrons are distributed around the nucleus.
  3. Bohr Model (1913): Niels Bohr suggested that electrons move in circular orbits around the nucleus.
    • Electrons can only occupy specific orbits with fixed energies.
    • Bohr’s model worked for hydrogen but didn’t explain the spectra of multi-electron atoms because it ignored the wave nature of electrons.

Quantum Mechanical Model

  • Heisenberg’s Uncertainty Principle: States that you can’t know both the exact position and the exact velocity of an electron at the same time. This contradicted Bohr’s model.
  • Schrödinger (1926): Developed the Schrödinger equation, which treats electrons as both particles and waves, resolving issues with the Bohr model.
    • Schrödinger’s equation describes electron distributions and the allowed energy levels in atoms.
    • This model is based on quantum mechanics and works with Heisenberg’s principle.

Quantum Mechanical Model of the Atom

  • Quantum numbers: The energy states of electrons are described by three quantum numbers:
    1. Principal Quantum Number (n): Describes the shell.
    2. Azimuthal Quantum Number (l): Describes the subshell.
    3. Magnetic Quantum Number (ml): Describes the orbital.
  • Schrödinger’s equation gives the allowed energy states (quantized) and the corresponding wave functions (mathematical descriptions) for electrons.
  • In multi-electron atoms, orbitals have different energies based on the values of n and l. The lower the sum of (n + l), the lower the energy of the orbital. If two orbitals have the same (n + l), the one with the lower n has a lower energy.

Electron Configuration and Filling of Orbitals

  • Electrons fill orbitals in order of increasing energy. This is governed by:
    • Pauli Exclusion Principle: No two electrons in an atom can have the same set of quantum numbers.
    • Hund’s Rule: Electrons fill orbitals of the same energy singly (one per orbital) before pairing up.

This leads to the formation of the electronic structure of atoms, explaining how electrons are arranged in shells, subshells, and orbitals.

Extra Insights for Competitive Exams:

  • Understanding the relationship between quantum numbers and energy levels is crucial for predicting the behavior of electrons.
  • Electron configurations help in predicting the chemical properties of elements, such as reactivity and bonding behavior.
  • Key points like Bohr’s model limitations, Heisenberg’s principle, and Schrödinger’s equation are important for solving higher-level questions.
  • Remember the Pauli Exclusion Principle and Hund’s Rule as they are central to understanding how electrons fill orbitals in multi-electron atoms.

This structure should help you understand the concepts better and solve competitive exam questions on atomic structure.

These all are the notes of chapetr 2 in chemistry. And after some time you get important questions and NCERT solutions HERE. *#THANKS FOR VISITING, VISIT AGAIN#* 😊