Question

The product of linear momentum and angular momentum of an electron of the hydrogen atom is proportional to $ \, n^{x}$ , where $x$ is

• A. $0$
• B. $1$
• C. $-2$
• D. $2$

Answer 1

Answer: (A)

Linear momentum = $mv \, = \, \frac{m c Z}{137 \, n}$
Angular momentum = $\frac{n h}{2 \, \pi }$
Given,
Linear momentum $\times $ angular momentum $ \propto \, n^{x}$
$\therefore \, \frac{m c Z}{137 \, n} \, \times \, \frac{n h}{2 \pi } \propto \, n^{x}$
$ \, n^{0} \propto \, n^{x}$
$\Rightarrow \, \, \, x=0$