Chapter 2 · Class 11-12 & JEE/NEET

Atomic Physics

50 topics in 16 parts

Full lessonClass 12 Physics · Dual Nature, Atoms and Nuclei

Key formulas

Bohr Quantization of Angular Momentum
$L = m v r = \frac{n h}{2\pi}, \quad n = 1, 2, 3...$
Radius of n-th Orbit
$r_n = 0.529 \,\frac{n^2}{Z} \text{ \AA} = \frac{n^2 h^2 \epsilon_0}{\pi m Z e^2}$
Energy of Electron in n-th Orbit
$E_n = -13.6 \,\frac{Z^2}{n^2} \text{ eV} \quad (K_n = -E_n, \; U_n = 2E_n)$
Rydberg Formula for Spectral Lines
$\frac{1}{\lambda} = R_H Z^2 \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right), \quad R_H \approx 1.097 \times 10^7 \text{ m}^{-1}$

Bohr energy levels Thomson-model oscillation frequency Rutherford impact parameter Distance of closest approach Rutherford differential cross-section Rutherford scattering count

Key ideas

Bohr Atomic Orbits and Hydrogen Spectral Series Transitions

4. Systematic Comparison & Parameter Classifications

Series Name	Lower State (n1)	Upper States (n2)	Spectral Region	Shortest Wavelength (Series Limit)
Lyman Series	n = 1	2, 3, 4...	Ultraviolet (UV)	λ_min = 1/R ≈ 912 Å
Balmer Series	n = 2	3, 4, 5...	Visible Spectrum	λ_min = 4/R ≈ 3646 Å
Paschen Series	n = 3	4, 5, 6...	Infrared (IR)	λ_min = 9/R ≈ 8204 Å
Brackett Series	n = 4	5, 6, 7...	Far Infrared	λ_min = 16/R ≈ 14585 Å
Pfund Series	n = 5	6, 7, 8...	Far Infrared	λ_min = 25/R ≈ 22790 Å

Exam Worked Example

Problem: Find the ratio of the longest wavelength in the Lyman series to the longest wavelength in the Balmer series for atomic Hydrogen.

● Step 1: Longest wavelength in Lyman series occurs for transition n = 2 → n = 1: 1/λ_L = R [1/1² - 1/2²] = 3R/4 → λ_L = 4/(3R).

● Step 2: Longest wavelength in Balmer series occurs for transition n = 3 → n = 2: 1/λ_B = R [1/2² - 1/3²] = 5R/36 → λ_B = 36/(5R).

● Step 3: Ratio λ_L / λ_B = [4/(3R)] / [36/(5R)] = (4/3) * (5/36) = 5 / 27 ≈ 0.185.

Checkpoint

1. If an electron in a hydrogen atom jumps from n = 3 to n = 1, how does its orbital kinetic energy change?

All 50 topics in Atomic Physics

Thomson's Atomic Model
- Thomson's Atomic Model
Rutherford Scattering
- Alpha Particle Scattering Experiment
- Impact Parameter & Scattering Angle
- Distance of Closest Approach & Nuclear Size
Bohr Model of Atom
- Postulates & Fundamental Hypotheses
- Hypothetical Atomic Energy Levels
- Radius of Stationary Orbits
- Velocity of Electron in Orbit
- Energy of Electron in Orbit
- Orbital Frequency & Period of Electron
- Angular Momentum Quantization
- Magnetic Moment & Magnetic Field of Revolving Electron
- De Broglie Matter Waves in Orbits
Hydrogen-like Atoms
- Single-Electron Hydrogenic Ions
- Atomic Number Scaling of Radius & Energy
- Positronium
Ionization Energy & Potential
- Standard Hydrogenic Ionization Energy
- Ionization From Excited States
Excitation Energy & Potential
- Standard Excitation Potentials
- Atomic Excitation Mechanisms
Binding Energy & Separation Energy
- Binding Energy
- Separation Energy
Limitations of Bohr's Atomic Model
- Multi-Electron Atom Limitations
- Sommerfeld Elliptic Orbits & Fine Structure
Wavelength of Photon Emitted in De-excitation
- Hydrogen Spectrum
- Hydrogen Spectral Series
- Number of Spectral Lines
- Emitted-Photon Wavelength & Frequency
Origin of Spectra
- Absorption Spectra
- Emission Spectra
- Fraunhofer Lines
Effect of Nucleus Motion on Energy of Atom
- Reduced Mass of Electron-Nucleus System
- Effect of Nuclear Mass on Bohr Model
Atomic Collision
- Excitation & Ionization by Electron Impact
- Collision of a Neutron With an Electron
- Franck-Hertz Experiment
Modified Bohr Model
- Custom Central Force Laws & Potentials
- Bohr Quantization for Non-Coulombic Systems
Photon Momentum & Recoil
- Recoil Velocity & Energy of Atom
- Momentum of Emitted & Absorbed Photons
X-rays
- Discovery
- Production in a Coolidge Tube
- Properties
- Continuous Spectrum & Cut-off Wavelength
- Characteristic Spectrum & Moseley's Law
- Absorption
- Spectral Origin
- Applications
Radiation Force & Pressure
- Force Exerted by Radiation on Atoms
- Radiation Pressure