Question

The ratio of the speed of an electron in the first orbit of hydrogen atom to that in the first orbit of $H{e}^{+}$ is

• A. 1 : 2
• B. 2 : 1
• C. 1 : 4
• D. 4 : 1

Answer 1

The correct option is A 1 : 2

The velocity of an electron in an orbit is given by
$v\propto \frac{Z}{n}$
Let the proportionality constant be $v_o$
Then $v=v_o\times \frac{Z}{n}$
$n=1$ is given in the problem.
Then,
$v_H=v_o$ (both $Z$ and $n=1$)
$v_{He}=2v_o$ ($Z=2$ and $n=1$)
Hence, $\frac{v_H}{v_{He}}=\frac{1}{2}$