The ratio of the speed of the electron in the | vedclass

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(D) The speed of an electron in the $n^{th}$ orbit of a hydrogen-like atom is given by the formula $v_n = v_0 \frac{Z}{n}$,where $Z$ is the atomic num

Vedclass · Accepted Answer

$2:1$

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(D) The speed of an electron in the $n^{th}$ orbit of a hydrogen-like atom is given by the formula $v_n = v_0 \frac{Z}{n}$,where $Z$ is the atomic number and $n$ is the principal quantum number.Since the principal quantum number $n$ is the same $(n=3)$ for both cases,the speed is directly proportional to the atomic number $Z$ $(v \propto Z)$.For $He^{+}$,the atomic number $Z_{He^+} = 2$.For the hydrogen atom $(H)$,the atomic number $Z_H = 1$.Therefore,the ratio of the speeds is $\frac{v_{He^+}}{v_H} = \frac{Z_{He^+}}{Z_H} = \frac{2}{1} = 2:1$.

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

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