Question

L_{n, z} = orbit angular momentum for $n^{th}$ orbit of hydrogen and hydrogen like species then calculate ratio of $\frac{L_{2,2}}{L_{3,3}}$

Answer 1

2/3

Answer 2

The angular momentum of an electron in the $n^{th}$ orbit is given by the formula $L_n = n \frac{h}{2\pi}$, where $n$ is the principal quantum number and $h$ is Planck's constant.

For $L_{2,2}$, the principal quantum number is $n=2$, so $L_{2,2} = 2 \frac{h}{2\pi}$. For $L_{3,3}$, the principal quantum number is $n=3$, so $L_{3,3} = 3 \frac{h}{2\pi}$.

The ratio is calculated as: $\frac{L_{2,2}}{L_{3,3}} = \frac{2 \frac{h}{2\pi}}{3 \frac{h}{2\pi}} = \frac{2}{3}$