Physics20785 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 sub shells? Label each state with the appropriate set of quantum numbers n, l, ml, ms. (c) Show that the number of states in a shell, that is, states having the same n, is given by 2n2. (Hint: 1+2+3+ldo
(a) How many atomic states are there in hydrogen with $n=3$? (b) How are they distributed among the sub shells? Label each state with the appropriate set of quantum numbers $n, l, m_l, m_s$. (c) Show that the number of states in a shell, that is, states having the same $n$, is given by $2n^2$. (Hint: $1+2+3+\ldots+n=\frac{n(n+1)}{2}$). [5]
- Principal quantum number: $n = 3$ - Quantum number rules: - $l = 0, 1, \dots, (n-1)$ - $ml = -l, \dots, 0, \dots, +l$ → $(2l+1)$ values - $ms = \pm\tfrac{1}{2}$ → 2 values --- $$\text{Total states} = 2n^2 = 2(3)^2 = 18 \text{ states}$$ --- For $n=3$, $l = 0, 1, 2$. Subshell 3s: $l = 0$ →