The ratio of velocity of electron in the seco | vedclass

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Question

(B) The velocity of an electron in the $n^{th}$ orbit of a hydrogen-like species is given by the formula $v = v_0 	imes \frac{Z}{n}$,where $v_0$ is a

Vedclass · Accepted Answer

$\frac{3}{5}$

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(B) The velocity of an electron in the $n^{th}$ orbit of a hydrogen-like species is given by the formula $v = v_0 	imes \frac{Z}{n}$,where $v_0$ is a constant,$Z$ is the atomic number,and $n$ is the orbit number.For $He^{+}$ $(Z_1 = 2)$ in the second orbit $(n_1 = 2)$: $v_1 = v_0 	imes \frac{2}{2} = v_0$.For $B^{4+}$ $(Z_2 = 5)$ in the third orbit $(n_2 = 3)$: $v_2 = v_0 	imes \frac{5}{3}$.The ratio of the velocities is $\frac{v_1}{v_2} = \frac{v_0}{v_0 	imes \frac{5}{3}} = \frac{3}{5}$.Thus,the correct option is $B$.

The ratio of velocity of electron in the second orbit of $He^{+}$ to the third orbit of $B^{4+}$ is $:-$

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