Physics20745 marksNumerical: hydrogen atomic states n=3space quantization and spin
(a). How many atomic states are there in hydrogen with n = 3? (b) How are they distributed among the subshells? Label each state with the appropriate set of quantum numbers n, 1, m, m (c) Show that the number of states in a shell, that is, states having the same n, is given by 2n22n^22n2.
(a). How many atomic states are there in hydrogen with n = 3? (b) How are they distributed among the subshells? Label each state with the appropriate set of quantum numbers n, 1, m, m (c) Show that the number of states in a shell, that is, states having the same n, is given by 2n22n^22n2. [5]
- Principal quantum number: $n = 3$ - Quantum number rules: - $l = 0, 1, \ldots, (n-1)$ - $ml = -l, \ldots, 0, \ldots, +l$ → $(2l+1)$ values - $ms = \pm\tfrac{1}{2}$ → 2 values --- For $n = 3$, $l = 0, 1, 2$. $$N = 2n^2 = 2(3)^2 = 18 \text{ states}$$ --- n l $ml$ $ms$ -------------------- 3 0 0