Question

The velocity of an electron in the first orbit of $H$ atom is ${}^{\prime }v{}^{\prime }$. The velocity of an electron in the second orbit of $H{e}^{+}$ is

• A. $2v$
• B. $v$
• C. $\frac{v}{2}$
• D. $\frac{v}{4}$

Answer 1

The correct option is B $v$

For hydrogen:

Angular momentum $=mvr=\frac{nh}{2\pi }$

$v=\frac{nh}{mr2\pi }$

$r=0.529\frac{n^2}{Z}$

So, $v=\frac{Zh}{0.529mn2\pi }$

For hydrogen $Z=1,n=1$

$v=\frac{h}{0.529m2\pi }$

For $H{e}^{+}$ $Z=2,n=2$

$v_1=\frac{2h}{0.529m\times 2\times 2\pi }=v$