• $summary_{type}$: revision
• $word_{count}$: 200

Essential formulas: $r_n$ = $n^2$$a_0$/Z ($a_0$ = 0.529 A). $v_n$ = Z$v_0$/n ($v_0$ = c/137). $E_n$ = -13.6*$Z^2$/$n^2$ eV. $L_n$ = nhbar (independent of Z). 1/lambda = R$Z^2$*(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$\frac{n-1}{2}$. 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$\frac{n-1}{2}$ 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 = nhbar is often the fastest route in problems. Modern physics topics contribute approximately 4% of JEE weightage, typically 1-2 MCQs.