Question

In a hydrogen atom following Bohr's postulates, the product of linear momentum and angular momentum is proportional to $(n{)}^x$ where $n$ is the orbit number. Then $x$ is

• A. $0$
• B. $2$
• C. $-2$
• D. $1$

Answer 1

The correct option is A $0$

According to Bohr's model of an atom:

Speed of the electron in nth orbit, $v_n=2.18\times {10}^6\frac{Z}{n}m/s$

Angular momentum of an electron in the nth orbit, $L_n=\frac{nh}{2\pi }$

Thus, $L_n\times \left(m{v}_n\right)=\frac{nh}{2\pi }\times m(2.18\times {10}^6)\frac{Z}{n}\propto n^0$

$⟹x=0$