Q76 / 90 · JEE Main 2022 (25 Jun Shift 1) · Physics

The ratio for the speed of the electron in the $3^{rd}$ orbit of ${He}^{+}$ to the speed of the electron in the $3^{rd}$ orbit of hydrogen atom will be :

Solution

The speed of electron is given by $v = 2.18 \times 10^{6} \times \frac{Z}{n} m s^{- 1}$ , where, $Z$ is atomic number and $n$ is number of orbit.

Now, for third orbit, ratio of speed of electron is $\frac{v_{H}}{v_{{He}^{+}}} = \frac{Z_{H}}{Z_{{He}^{+}}} = \frac{1}{2}$

$\Rightarrow \frac{v_{{He}^{+}}}{v_{H}} = \frac{2}{1}$

Hence, the correct answer is option: 'D'.