$word_{count}$: 220

Four quantum numbers define each electron's state: (1) n (principal): 1,2,3... — shell, energy, size. Shell has n subshells, $n^2$ orbitals, 2$n^2$ electrons. (2) l (azimuthal): 0 to n-1 — subshell shape. l=0(s), 1(p), 2(d), 3(f). Orbital angular momentum = sqrt(l(l+1))h-bar. Subshell has 2l+1 orbitals, 2(2l+1) electrons. (3) $m_l$ (magnetic): -l to +l — orbital orientation. 2l+1 values. (4) $m_s$ (spin): +1/2 or -1/2 — intrinsic angular momentum. Pauli exclusion: no two electrons share all four quantum numbers. Validity check: l < n (NOT <=), |$m_l$| <= l, $m_s$ = +/-1/2. Node counting: radial = n-l-1, angular = l, total = n-1. Orbital shapes: s (spherical), p (dumbbell), d (cloverleaf, except dz2), f (complex). s orbitals have finite probability density at the nucleus; p, d, f have nodes at the nucleus. Penetration order: s > p > d > f for same n. In multi-electron atoms, energy depends on both n and l (s < p < d < f for same n). In hydrogen, energy depends only on n.