[ -\frac\hbar^22m\fracd^2\psidx^2 + V(x)\psi = E\psi ]
Slater’s rules (approximate).
Example: Ionization energy of Li (Z=3): Remove 2s electron.
Electron config: ( 1s^2 2s^1 ).
Slater: ( Z_\texteff ) for 2s ≈ 3 - (2×0.85) = 1.30
( IE \approx 13.6 \times (1.30)^2 / 2^2 = 13.6 \times 1.69 / 4 = 5.75\ \texteV ) (actual: 5.39 eV) Solucionario Fisica Cuantica Eisberg Resnick
Cuando tu respuesta difiera de la del solucionario, no asumas que tú estás mal (recuerda que muchos solucionarios son manuscritos no oficiales). Revisa las unidades, los órdenes de magnitud y las aproximaciones. A veces, el solucionario asume ciertos valores constantes (como la masa del electrón) diferentes a los que tú usaste.
Find wavelength for ( n=2 \to n=1 ) in hydrogen. [ \frac1\lambda = 1.097\times 10^7\left( 1 - \frac14 \right) = 1.097\times 10^7 \times \frac34 = 8.2275\times 10^6\ \textm^-1 ] [ \lambda = 121.5\ \textnm ] Photons and the Photoelectric Effect:
[ B = (Zm_p + Nm_n - M_\textnucleus)c^2 ]
Example: ( ^4_2\textHe ) (mass = 4.002603 u).
( Z=2, N=2 ):
( 2(1.007276) + 2(1.008665) = 4.031882\ \textu )
Mass defect ( \Delta m = 0.029279\ \textu )
( B = 0.029279 \times 931.5\ \textMeV/u = 27.3\ \textMeV )
Binding energy per nucleon = ( 27.3/4 = 6.82\ \textMeV ) Rutherford-Bohr Model of the Atom:
For Students: The manual is essential for self-study. The text is verbose and the problems are often open-ended. The solution manual provides the "sanity check" needed to ensure the student has chosen the correct approximations.
For Educators: The manual assists in selecting problems for assignments. By reviewing the complexity of the solution, an instructor can gauge how long a problem will take to solve and what prerequisite math skills (e.g., complex analysis, partial derivatives) are required.