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Essential formulas: r_n = n^2a_0/Z (a_0 = 0.529 A). v_n = Zv_0/n (v_0 = c/137). E_n = -13.6Z^2/n^2 eV. L_n = nhbar (independent of Z). 1/lambda = RZ^2(1/n_f^2 - 1/n_i^2), R = 1.097 x 10^7 m^-1. KE = -E, PE = 2E (virial theorem). Spectral lines from level n: n(n-1)/2. First excitation energy = 10.2 eV. lambda_min (X-ray) = 12400/V Angstrom.

JEE strategy: (1) For ratio problems, use proportionality relations (r proportional to n^2/Z, E proportional to Z^2/n^2) — don't substitute numbers until the final step. (2) For spectral line problems, first determine which series (identify n_f), then apply Rydberg formula. (3) Remember n(n-1)/2 for counting lines. (4) For hydrogen-like ion comparisons, find which transitions give matching energies using Z^2*(1/n_f^2 - 1/n_i^2). (5) For excitation problems, distinguish photon absorption (exact energy match required) from electron collision (any energy above threshold). (6) The Bohr model gives correct energies only for one-electron systems. (7) Angular momentum quantization L = n*hbar is often the fastest route in problems. Modern physics topics contribute approximately 4% of JEE weightage, typically 1-2 MCQs.