Modern Physics Revision Notes for JEE Main

Photoelectric Effect

• Einstein's equation: $KE_{max} = h\nu - \phi = h(\nu - \nu_0)$.
• Stopping potential $V_0$: $eV_0 = h\nu - \phi$.
• Threshold frequency $\nu_0 = \phi/h$; threshold wavelength $\lambda_0 = hc/\phi$.
• Intensity ↔ number of photons; frequency ↔ energy per photon.
• Saturation current ∝ intensity; $V_0$ independent of intensity.

de Broglie Waves

• $\lambda = h/p = h/\sqrt{2mKE}$.
• Electron accelerated through $V$ volts: $\lambda = 12.27/\sqrt V$ Å.
• Davisson–Germer confirmed matter waves.

Bohr Model (H-like)

• $r_n = 0.529, n^2/Z$ Å; $v_n = 2.19\times 10^6 Z/n$ m/s.
• $E_n = -13.6, Z^2/n^2$ eV; ionisation energy = $13.6 Z^2$ eV.
• Rydberg: $1/\lambda = R Z^2(1/n_1^2 - 1/n_2^2)$, $R = 1.097\times 10^7$ m⁻¹.
• Series: Lyman (UV, $n_1=1$), Balmer (visible, $n_1=2$), Paschen/Brackett/Pfund (IR).
• Number of spectral lines from level $n$: $n(n-1)/2$.

X-rays

• Continuous X-rays: bremsstrahlung; cutoff $\lambda_{min} = hc/eV$.
• Characteristic X-rays: Moseley's law $\sqrt\nu = a(Z-b)$.

Nuclear Physics

• Mass defect $\Delta m$; binding energy $BE = \Delta m c^2$. Use 1 u = 931.5 MeV.
• Radioactive decay: $N = N_0 e^{-\lambda t}$, half-life $T_{1/2} = 0.693/\lambda$, mean life $\tau = 1/\lambda$.
• Activity $A = \lambda N$; SI unit Bq, practical unit Ci = 3.7×10¹⁰ Bq.
• α decay: $Z \to Z-2, A\to A-4$. β⁻: $Z\to Z+1$. γ: no change.
• Q-value = (mass reactants − mass products)×931.5 MeV.

Common Numeric Shortcuts

• Photon energy in eV = $1240/\lambda(\text{nm})$.
• Any H-line wavelength (nm) = $91.13/(1/n_1^2 - 1/n_2^2)$.
• After $n$ half-lives, fraction left = $1/2^n$.

Practice MCQs

Q1. Threshold wavelength of a metal is 500 nm. Light of 400 nm will produce photoelectrons with maximum KE (in eV) of about A) 0.31 B) 0.62 C) 1.24 D) 2.48

Q2. An electron accelerated through 150 V has de Broglie wavelength closest to A) 1.00 Å B) 0.50 Å C) 2.00 Å D) 0.25 Å

Q3. For a hydrogen atom, ratio of radii of second and first Bohr orbits is A) 2 B) 4 C) 1/2 D) 1/4

Q4. Number of spectral lines emitted when hydrogen atoms de-excite from n = 5 to ground state is A) 5 B) 10 C) 15 D) 20

Q5. The stopping potential in a photoelectric experiment depends on A) Intensity only B) Frequency only C) Both intensity and frequency D) Neither

Q6. If half-life of a nucleus is 20 min, fraction remaining after 1 h is A) 1/2 B) 1/4 C) 1/8 D) 1/16

Q7. Binding energy per nucleon is maximum for A) ²H B) ⁵⁶Fe C) ²³⁵U D) ⁴He

Q8. Moseley's law relates √ν to A) A B) Z C) n D) λ

Q9. A γ-ray photon has energy 1.022 MeV. Its momentum equals A) 1.022 MeV/c B) 0.511 MeV/c C) 2.044 MeV/c D) zero

Q10. In β⁻ decay, which of these is emitted along with the electron? A) Neutrino B) Antineutrino C) Photon only D) Positron

Answers: 1-B (hc/λ − hc/λ₀ = 1240/400 − 1240/500 = 3.1 − 2.48 = 0.62 eV.), 2-A (λ = 12.27/√150 ≈ 1.00 Å.), 3-B (rₙ ∝ n²; r₂/r₁ = 4.), 4-B (n(n−1)/2 = 10.), 5-B (V₀ depends on ν and work function.), 6-C (3 half-lives → 1/8.), 7-B (Fe-56 sits at the peak of the BE/A curve.), 8-B (√ν = a(Z − b).), 9-A (p = E/c for photons.), 10-B (β⁻ produces an electron + antineutrino.)

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