Last Updated: April 2026
NEET modern physics 2027 aspirants — Modern Physics (Dual Nature, Atoms, Nuclei, Semiconductors) is a 12–15 mark zone in NEET-UG. The 2026 NEET-UG paper had 5 questions from this block (1 photoelectric, 2 atomic structure, 1 mass-defect, 1 semiconductor diode). Average marks-per-minute here is among the highest in NEET Physics: short formulas, large weightage. With NEET 2026 cutoff for general candidates at 162/720, even one slip in this scoring block is fatal.
1. Dual Nature of Radiation — Photoelectric Effect
Hertz observed photoelectric emission (1887). Einstein (1905) explained it using photon hypothesis: E = hν. Each photon transfers all-or-nothing energy to one electron.
Einstein’s Photoelectric Equation
KE_max = hν − φ where φ = work function. In terms of stopping potential V₀: eV₀ = hν − φ. Plot of V₀ vs ν: slope = h/e, x-intercept = ν₀ (threshold frequency).
Worked Example 1
Q. Light of wavelength 400 nm falls on a metal of work function 2.0 eV. Find KE_max.
Sol. E = hc/λ = (1240 eV·nm)/400 nm = 3.1 eV. KE_max = 3.1 − 2.0 = 1.1 eV.
Worked Example 2
Q. Threshold wavelength is 600 nm. What is the work function?
Sol. φ = hc/λ₀ = 1240/600 = 2.07 eV.
2. de Broglie Hypothesis — Matter Waves
Wavelength of a particle: λ = h/p = h/(mv). For a charged particle accelerated through potential V: λ = h/√(2meV). For an electron: λ (in nm) = 1.227/√V.
Worked Example 3
Q. Find de Broglie wavelength of electron at 100 V.
Sol. λ = 1.227/√100 = 0.1227 nm (close to interatomic spacing — basis for electron diffraction in Davisson-Germer).
3. Bohr Model of Hydrogen Atom
Three postulates: (1) circular stable orbits, (2) angular momentum mvr = nh/2π, (3) energy emitted/absorbed only on transition.
Key Formulas
- Radius: r_n = 0.529 × n² / Z Å
- Velocity: v_n = (c/137) × Z/n
- Energy: E_n = −13.6 × Z²/n² eV
- Wavenumber: 1/λ = R(1/n₁² − 1/n₂²), R = 1.097×10⁷ m⁻¹
Worked Example 4
Q. Find energy of electron in 2nd Bohr orbit of H.
Sol. E₂ = −13.6/4 = −3.4 eV.
Worked Example 5
Q. Wavelength of first line of Lyman series of H?
Sol. 1/λ = R(1 − 1/4) = 3R/4 → λ = 4/(3R) = 121.6 nm (UV).
4. Spectral Series of Hydrogen
| Series | n_final | Region | Discovered |
|---|---|---|---|
| Lyman | 1 | UV | 1906 |
| Balmer | 2 | Visible | 1885 |
| Paschen | 3 | IR | 1908 |
| Brackett | 4 | IR | 1922 |
| Pfund | 5 | Far IR | 1924 |
5. Nuclei — Mass Defect, Binding Energy
Mass defect Δm = Zm_p + (A−Z)m_n − M_nucleus. Binding energy BE = Δmc². 1 amu = 931.5 MeV.
Worked Example 6
Q. Δm = 0.0437 amu for ⁴He. Find BE per nucleon.
Sol. BE = 0.0437 × 931.5 = 40.7 MeV. Per nucleon = 40.7/4 = 10.18 MeV.
6. Radioactive Decay
N = N₀e^(−λt); half-life T_½ = 0.693/λ; mean life τ = 1/λ. Activity A = λN.
Worked Example 7
Q. Half-life of a radioisotope is 5 years. What fraction remains after 15 years?
Sol. 15/5 = 3 half-lives → (1/2)³ = 1/8 (12.5%).
Worked Example 8
Q. Activity drops from 8000 Bq to 1000 Bq in 30 minutes. Find half-life.
Sol. 8000/1000 = 8 = 2³ → 3 half-lives → T_½ = 30/3 = 10 minutes.
7. Constants Master Table
| Quantity | Symbol | Value | Use |
|---|---|---|---|
| Planck constant | h | 6.626×10⁻³⁴ J·s | E = hν |
| hc product | hc | 1240 eV·nm | E = hc/λ shortcut |
| Rydberg constant | R | 1.097×10⁷ m⁻¹ | Hydrogen spectrum |
| Electron mass | m_e | 9.11×10⁻³¹ kg | de Broglie, kinetics |
| Specific charge | e/m | 1.76×10¹¹ C/kg | Thomson experiment |
| Electron charge | e | 1.6×10⁻¹⁹ C | eV conversion |
| amu equivalent | 1u | 931.5 MeV | Binding energy |
| Bohr radius | a₀ | 0.529 Å | Atomic dimensions |
| Hydrogen ground E | E₁ | −13.6 eV | Energy levels |
8. 35 NEET Practice Problems (Selected)
- Q1. Photoelectric current depends on — intensity. (threshold-frequency dependence is for emission, not magnitude of saturation current).
- Q2. Stopping potential depends on frequency only.
- Q3. Photon momentum p = h/λ.
- Q4. de Broglie wavelength of α-particle accelerated through V volts is λ = h/√(2·m_α·q_α·V).
- Q5. Energy of 2nd excited state of H = E₃ = −1.51 eV.
- Q6. Number of spectral lines from n=4: 4·3/2 = 6.
- Q7. Bohr’s model fails for — multi-electron atoms (does not explain fine structure).
- Q8. α-decay: ²³⁸U → ²³⁴Th + ⁴He. Q-value = (M_U − M_Th − M_He)c².
- Q9. β-decay: neutron → proton + e⁻ + ν̄. Mass number unchanged.
- Q10. γ-emission: no change in A or Z; just de-excitation.
- Q11. Average BE per nucleon peaks ~8.8 MeV near A = 56 (Fe).
- Q12. Both fission and fusion release energy because BE/nucleon increases.
- Q13. Compton effect demonstrated photon momentum.
- Q14. Davisson-Germer demonstrated wave nature of electron.
- Q15. Stopping potential vs frequency: slope = h/e ~ 4.14×10⁻¹⁵ V·s.
- Q16. Wavelength of Hα (Balmer first) = 656 nm.
- Q17. ⁴He nucleus has 2 protons + 2 neutrons. Density ≈ 2.3×10¹⁷ kg/m³ (independent of A).
- Q18. Activity of 1 g of ²²⁶Ra ~ 3.7×10¹⁰ Bq = 1 Ci.
- Q19. Quantum efficiency of photo-cell ≪ 1.
- Q20. X-rays produced by transitions in inner shells; characteristic K-α from L→K transition.
- Q21. Cyclotron frequency f = qB/(2πm). Independent of velocity (non-relativistic).
- Q22. Moseley’s law: √ν = a(Z − b). Linked frequency to atomic number.
- Q23. Nuclear radius: R = R₀A^(1/3), R₀ = 1.2 fm.
- Q24. Ionisation energy of H = 13.6 eV (energy to remove electron from n=1 to ∞).
- Q25. Hydrogen-like ion energy E = −13.6 Z²/n². For He⁺ (Z=2), E₁ = −54.4 eV.
- Q26. Pair production: γ → e⁻ + e⁺ requires E_γ ≥ 1.022 MeV.
- Q27. Threshold of photoelectric emission for Cs (φ = 2.0 eV) → λ_max = 1240/2 = 620 nm.
- Q28. Photon flux × E per photon = total power (P = N·hν).
- Q29. Graph of N vs t for radioactivity is exponential decay.
- Q30. Energy released in fission of one ²³⁵U = ~200 MeV.
- Q31. Energy released in D-T fusion: ²H + ³H → ⁴He + n + 17.6 MeV.
- Q32. Critical mass — minimum mass of fissile material to sustain chain reaction.
- Q33. Moderators in reactors slow neutrons (graphite, heavy water).
- Q34. Control rods absorb neutrons (cadmium, boron).
- Q35. Solar energy comes from p-p chain fusion: 4 ¹H → ⁴He + 2e⁺ + 2ν + 26.7 MeV.
9. NEET Strategy for Modern Physics
Memorise the constants table and the Bohr formulas — they recur every year. Practise photoelectric numericals daily. Use NEET Gurukul Free Resources for previous-year questions and join our Physics intensive. Build your NEET 2027 plan with at least 200 MCQs from this block before mocks.
FAQ
Q1. Why doesn’t classical physics explain photoelectric effect?
Classically, a wave should heat the surface — emission should occur at all frequencies given enough intensity, with delay. Experiments show emission is instantaneous and frequency-thresholded. Only photon (quantum) picture explains this.
Q2. Difference between α, β, γ?
α = ⁴He nucleus (heavy, +2, low penetration). β = electron/positron (medium). γ = photon (no mass/charge, highest penetration).
Q3. Why does BE/nucleon increase from H to Fe and decrease beyond?
Up to Fe (A≈56), strong nuclear attraction dominates. Beyond, repulsion among many protons reduces stability.
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