JEE Main Modern Physics 2027 — Photoelectric Effect, Atomic Models, Nuclear Physics and 40 Practice Problems

Last Updated: May 2026

JEE Main Modern Physics 2027 yields 3–4 questions = 12–16 marks per paper — among the top-3 highest-yield Physics chapters. The unit covers Class 12 Chapters 11–13 (Dual Nature of Radiation, Atoms, Nuclei). This 1,800-word JEE Main Modern Physics 2027 guide covers photoelectric effect, de Broglie waves, Bohr’s model, hydrogen spectrum, mass defect, binding energy, radioactive decay laws, and 40 practice problems calibrated to JEE Main difficulty.

1. Photoelectric Effect

Einstein’s equation: hν = Φ₀ + (1/2)mv²ₘₐₓ, where Φ₀ = work function. Threshold frequency ν₀ = Φ₀/h. Stopping potential V₀: eV₀ = (1/2)mv²ₘₐₓ.

Key facts: KE depends on frequency, not intensity. Number of photoelectrons depends on intensity. No emission below ν₀ — instantaneous emission above.

2. de Broglie Hypothesis

Wavelength of matter wave: λ = h/p = h/(mv) = h/√(2mE) = h/√(2meV). For an electron through potential difference V: λ = 12.27/√V Å.

3. Davisson-Germer Experiment

Confirmed wave nature of electron through diffraction at Ni crystal at 54V → λ = 1.67Å (theory) ≈ 1.65Å (experiment).

4. Bohr’s Model of Hydrogen Atom

Hydrogen Spectrum

Rydberg formula: 1/λ = R·Z²·(1/n₁² – 1/n₂²), R = 1.097×10⁷ m⁻¹.

5. Atomic Nucleus

• Radius R = R₀·A^(1/3), R₀ = 1.2 fm.
• Nuclear density ≈ 2.3×10¹⁷ kg/m³ — independent of A.
• Mass defect: Δm = Z·mₚ + N·mₙ – M(nucleus).
• Binding energy: BE = Δm·c² = Δm·931.5 MeV (when Δm in u).
• BE/A peaks at Fe (≈8.8 MeV/nucleon). Fission of heavy nuclei + fusion of light nuclei → energy release.

6. Radioactive Decay Law

dN/dt = -λN → N = N₀·e^(-λt). Half-life T₁/₂ = ln 2/λ = 0.693/λ. Mean life τ = 1/λ. After n half-lives, fraction remaining = (1/2)ⁿ.

Decay types: α-decay (loses 2p+2n; Z→Z-2, A→A-4); β⁻-decay (n→p+e⁻+ν̄; Z→Z+1); β⁺-decay (p→n+e⁺+ν; Z→Z-1); γ-decay (excited nucleus → ground state).

7. Nuclear Reactions

• Fission: ²³⁵U + n → ¹⁴¹Ba + ⁹²Kr + 3n + ~200 MeV.
• Fusion: 4(¹H) → ⁴He + 2e⁺ + 2ν + ~26.7 MeV (sun’s energy).
• Q-value: Q = (mᵢ – m_f)·c². Positive Q → exothermic.

8. Important Constants

9. Common Question Patterns (JEE Main 2024–2025)

• Stopping potential — given frequency, work function, find V₀.
• Bohr radius/energy ratio for He+, Li²+ vs H.
• Wavelength shortest/longest in Lyman/Balmer series.
• Half-life and remaining nuclei after t.
• BE per nucleon comparison.

10. 40 Practice Problems (Sample 10)

1. If frequency doubles in photoelectric effect (above ν₀), KE: (a) doubles (b) halves (c) more than doubles (d) unchanged — (c)
2. de Broglie wavelength of an electron at 100 V: (a) 12.27 Å (b) 1.227 Å (c) 0.1227 Å (d) 122.7 Å — (b)
3. Energy of n=2 of He⁺: (a) -3.4 eV (b) -13.6 eV (c) -54.4 eV (d) -27.2 eV — (b)… actually He⁺ Z=2, E₂ = -13.6×(4/4) = -13.6 eV — (b)
4. Radius of orbit n=3 in H: (a) 0.529 Å (b) 1.587 Å (c) 4.76 Å (d) 9.52 Å — (c)
5. Lyman series lies in: (a) IR (b) Visible (c) UV (d) Microwave — (c)
6. Half-life of Po-210 is 138 days. Mass remaining of 1g after 414 days: (a) 1g (b) 0.5g (c) 0.25g (d) 0.125g — (d)
7. BE per nucleon is maximum for: (a) Hydrogen (b) Iron (c) Uranium (d) Helium — (b)
8. α-particle is emitted: A and Z change: (a) A-4, Z-2 (b) A-4, Z+2 (c) A, Z-2 (d) A-2, Z-2 — (a)
9. Energy released per fission of U-235: (a) 26 MeV (b) 200 MeV (c) 931 MeV (d) 2.2 MeV — (b)
10. Wavelength of K_α X-ray follows Moseley’s law: ν = a(Z-b)². The b for K_α is: (a) 1 (b) 2 (c) 0 (d) 3 — (a)

Frequently Asked Questions

Q1. Modern Physics — JEE Main weightage?

3–4 questions = 12–16 marks. Top-3 chapters in Physics by yield.

Q2. Bohr model is for which atoms?

Hydrogen-like (1 electron) systems: H, He⁺, Li²⁺, Be³⁺. Not multi-electron.

Internal Resources

• JEE Main Thermodynamics
• JEE Main Rotational Motion
• JEE Main Waves and Sound
• Free JEE Mock Test

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