Part of JPH-01 — Modern Physics: Photoelectric Effect & Matter Waves

Key Formulas and JEE Strategy

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Essential formulas: E = hf = hc/λ = 1240/λ(nm) eV. p = h/λ = E/c. Einstein: KE_max = hf - φ = eV0V_{0}. V0V_{0} slope = h/e. λ_dB = h/(mv) = h/√(2mKE) = 12.27/√V Å (electron). Uncertainty: \Delta x$$\Delta p ≥ ℏ/2. Compton: Δ\Deltaλ = (h/mc)(1-cosθ). Radiation pressure: I/c (absorb), 2I/c (reflect).

JEE strategy: (1) For photoelectric problems, always calculate E in eV first using 1240/λ, compare with φ, then find V0V_{0} = E - φ. (2) For de Broglie problems, identify what's constant (KE, momentum, speed, or voltage) before comparing wavelengths. (3) Remember the distinction: same KE → λ ∝ 1/√m; same p → same λ; same v → λ ∝ 1/m. (4) For graph problems, know the five key photoelectric graphs — especially V0V_{0} vs f (linear, slope h/e). (5) For uncertainty problems, apply \Delta x$$\Delta p = ℏ/2 and find KE = (Δp\Delta p)^{2}/(2m). (6) The photon always has more energy than an electron at the same wavelength, and longer wavelength at the same energy. Modern physics carries ~4% JEE weightage, typically 1-2 MCQs plus possible numerical.

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