Modern Physics
Why This Chapter Matters
Modern Physics covers photoelectric effect, Bohr model, nuclear physics, and semiconductors — 8-12 marks in JEE every year. This is the last chapter of Physics but always present in the exam.
Core Concepts
1. Photoelectric Effect
When light hits a metal surface, electrons are emitted IF frequency ≥ threshold.
Einstein's equation: KE_max = hf - φ = hf - hf₀
h = 6.626×10⁻³⁴ J·s (Planck's constant)
φ = work function (energy needed to remove electron from surface)
f₀ = threshold frequency = φ/h
Key observations:
2. de Broglie Wavelength
Every particle has associated wavelength: λ = h/p = h/mv
For electron accelerated through V volts: λ = h/√(2meV) = 1.23/√V nm
3. Bohr Model of Hydrogen
Electrons orbit in discrete circular orbits without radiating.
Quantisation: L = mvr = nh/2π = nℏ (n = 1, 2, 3...)
Orbit radius: r_n = n²a₀ (a₀ = 0.53 Å = Bohr radius)
Energy: E_n = -13.6/n² eV (negative → bound state)
Velocity: v_n = v₁/n (v₁ = 2.2×10⁶ m/s)
Energy of emitted photon: ΔE = E_final - E_initial = hf = hc/λ
Rydberg formula: 1/λ = R_H(1/n₁² - 1/n₂²) (R_H = 1.097×10⁷ m⁻¹)
Spectral series: Lyman (n₁=1, UV), Balmer (n₁=2, visible), Paschen (n₁=3, IR)
4. X-Rays
Characteristic X-rays: from electron transitions in inner shells. Specific to element.
Continuous X-rays (Bremsstrahlung): from deceleration of electrons.
Minimum wavelength: λ_min = hc/eV (V = accelerating voltage)
Moseley's law: √f = a(Z - b) (relates characteristic X-ray frequency to atomic number Z)
5. Nuclear Physics
Mass number A = protons + neutrons. Atomic number Z = protons.
Binding energy: BE = [Zm_p + (A-Z)m_n - M_nucleus]c²
Radioactive decay: N = N₀e^(-λt) = N₀(1/2)^(t/T₁/₂)
T₁/₂ = ln2/λ = 0.693/λ (half-life)
Activity: A = λN = A₀e^(-λt)
Types: α decay (A-4, Z-2), β⁻ decay (A, Z+1), β⁺ decay (A, Z-1), γ (A,Z unchanged)
6. Semiconductors (Brief)
Intrinsic: pure semiconductor (Si, Ge). Some e-h pairs by thermal excitation.
n-type: doped with pentavalent (P, As) → excess electrons
p-type: doped with trivalent (B, Al) → excess holes
p-n junction: depletion region, forward bias (current flows), reverse bias (no current)
PYQs
2024: Metal with work function 2 eV illuminated by photons of energy 5 eV. KE_max and stopping potential?
KE_max = 5-2 = 3 eV. Stopping potential V₀ = 3V.
2023: Hydrogen electron jumps from n=3 to n=1. Wavelength of emitted photon?
1/λ = R_H(1/1² - 1/3²) = R_H(1 - 1/9) = 8R_H/9
λ = 9/(8×1.097×10⁷) = 102.6 nm (UV, Lyman series)
2022: Radioactive sample T₁/₂ = 10 days. After 30 days, fraction remaining?
Fraction = (1/2)^(30/10) = (1/2)³ = 1/8