Modern Physics Lecture Notes

Introduction to Modern Physics

• Last topic of physics; important for JEE Main and NEET.
• Modern physics often taught at the end of the syllabus; students may struggle with it.
• 4-5 chapters in the modern physics checklist.
• Focus on atomic physics in today's lecture.

Atomic Physics Overview

• Atomic structure is crucial for understanding the atom.
• Questions in both physics and chemistry arise from atomic structure.
• Physics delves deeper than chemistry, including concepts like the Schrödinger equation.
• Coverage: JEE Main, NEET, and up to JEE Advanced level.
• Students should create a concept checklist using prior year questions and the provided checklist.

Models of Atomic Structure

1. Thomson's Model:

   • Called the plum pudding model.
   • Atom is a spherical ball with positive charge uniformly scattered and electrons as negative charges (like seeds in watermelon).
   • No nucleus concept; explains neutrality of atoms.

2. Rutherford's Model:

   • Based on alpha scattering experiment.
   • Majority of atom's space is empty; electrons revolve around a concentrated positive nucleus.
   • Introduced the concept of the nucleus.
   • Suggested electrons would lose energy and spiral into the nucleus, based on Maxwell's theory.

3. Bohr's Model:

   • First successful model addressing Rutherford's limitations.
   • Introduces three postulates:
     1. Electrons revolve in stable orbits without radiating energy.
     2. Electrons can only revolve in quantized orbits (stable energy levels).
     3. Energy is emitted or absorbed when electrons transition between orbits.

Bohr's Atomic Model: Three Postulates

• First Postulate: Stable circular motion without radiating energy.
  • Relation involving Coulomb force and centripetal force.
• Second Postulate: Angular momentum is quantized.
  • Condition: mvr = n(h/2π), where n is an integer.
• Third Postulate: Energy emitted during electron transition.
  • Relationship: E = E_n2 - E_n1 = hν = hc/λ.

Key Properties of Electrons in Bohr's Model

• Radius of nth Orbit: R_n = (n²h²)/(4π²kZem).
• Velocity of Electron: V_n = (2πkZ)/(nh).
• Angular Velocity: ω_n = V_n/R_n proportional to Z²/n³.
• Frequency of Revolution: f_n = ω_n/(2π) proportional to Z²/n³.
• Time Period: T_n = 1/f_n proportional to n³/Z².
• Current in nth Orbit: I_n = e * f_n.
• Magnetic Induction: B = (μ₀I)/(2R) proportional to Z³/n⁵.
• Magnetic Moment: μ = (eh)/(4πm).
• Energy of Electron: E_n = -13.6Z²/n² eV.*

Energy Levels in Hydrogen Atom

• First five energy levels:
  • E(1) = -13.6 eV
  • E(2) = -3.4 eV
  • E(3) = -1.51 eV
  • E(4) = -0.85 eV
  • E(5) = -0.54 eV
• Energy gaps decrease as n increases.
• Photon Emission: From higher to lower orbit releases energy equal to the energy difference.

Excitation and Ionization

• Excitation: Transition from lower to higher energy level.
• Ionization: Ejection of an electron when energy exceeds ionization potential.

Frequency and Wavelength of Emitted Radiation

• Relation: 1/λ = RZ²(1/n₁² - 1/n₂²).
• Rydberg's Formula: Used to calculate wavelengths of emitted radiation.

De-excitation of Atoms

• Excited electrons return to lower energy levels, emitting photons.
• Spectral lines correspond to the energy differences.

Hydrogen Spectrum and Spectral Series

• Spectral series classified based on electron transitions:
  • Lyman Series: Transitions to n=1.
  • Balmer Series: Transitions to n=2.

Effects of Nuclear Mass on Bohr Model

• When considering nuclear mass, apply reduced mass concept.
• Adjust equations to account for the nucleus's movement.

Conclusion

• Review all concepts thoroughly; ensure clarity on atomic structure.
• Utilize concept checklists and previous year questions for effective preparation.