Modern Physics Lecture Notes

Introduction to Modern Physics

• Modern physics is often taught at the end of the physics syllabus.
• Topics include atomic physics, important for JEE Main and NEET.
• Atomic structure is essential for understanding atoms and is interconnected with chemistry.

Atomic Physics Overview

• Focus on atomic structure to grasp deeper concepts beyond chemistry.
• The course will cover key points from JEE Main to JEE Advanced levels.
• Students should prepare a checklist with previous year questions.

Key Models of Atomic Structure

1. Thomson's Model

   • Described atom as a spherical ball with positive charge spread uniformly and electrons distributed like seeds in a watermelon.
   • No nucleus concept; it explained neutral behavior of atoms.

2. Rutherford's Model

   • Based on alpha particle scattering experiment on gold foil.
   • Discovered nucleus; electrons orbit around a dense, positively charged nucleus.
   • Predicted that electrons radiate energy and spiral into the nucleus, a limitation of this model.

3. Bohr's Model

   • Addressed Rutherford's limitations through three postulates.
   • Explained stable electron orbits without energy loss.
   • Introduced quantized orbits where electrons can only exist in specific energy levels.

Bohr's Atomic Model

Postulates of Bohr's Model

1. First Postulate

   • Electrons revolve around the nucleus in a stable orbit without radiating energy.
   • Force from nuclear charge provides centripetal force for circular motion.

2. Second Postulate

   • Electrons can only occupy quantized orbits, defined by quantized angular momentum:
     mv_r = n(h/2π)
   • Angular momentum must be integral multiple of h/2π.

3. Third Postulate

   • Energy is emitted when electrons transition between orbits. The energy emitted corresponds to the difference between the two orbits:
     E = E_n2 - E_n1 = hν = hc/λ

Properties of Electrons in Bohr Model

• Radius of nth orbit:
  R_n = (n^2h^2)/(4π^2kZ)
• Velocity of electron in nth orbit:
  v_n = (2πkZ)/(nh)
• Angular velocity:
  ω_n ∝ Z^2/n^3
• Time period of revolution:
  T_n ∝ n^3/Z^2
• Current due to revolving electron:
  I_n ∝ Z^2/n^3
• Magnetic moment of nth orbit:
  μ_n = (eh)/(4πm)
• Energy of electron in nth orbit:
  E_n = -13.6 eV * (Z^2/n^2)*

Energy Levels and Spectral Series

• Energy levels become closely spaced as n increases.
• Excitation and Ionization:
  • Excitation: Transition from a lower to a higher energy level.
  • Ionization: Energy required to remove an electron entirely from the atom.

Frequency and Wavelength of Emitted Radiation

• Emission occurs when an electron transitions from a higher to lower energy level.
• Rydberg's Formula:
  1/λ = RZ^2(1/n1^2 - 1/n2^2)
• Energy and wavelength relations:
  E = hc/λ

Atomic Collisions

• Collisions can supply energy for excitation or ionization.
• The impact parameter determines how much energy is transferred to the electron.
• Collisions can result in a range of energies being transferred.

Conclusion

• Understanding these concepts is essential for solving problems in JEE and NEET.
• Prepare a detailed checklist based on these notes and previous year questions for revision.
• Emphasize on grasping concepts to solve problems efficiently.