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(C) The velocity of an electron in the $n^{th}$ Bohr orbit is given by the formula $v = v_0 \frac{Z}{n}$, where $Z$ is the atomic number and $n$ is th

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$1: 3$

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(C) The velocity of an electron in the $n^{th}$ Bohr orbit is given by the formula $v = v_0 \frac{Z}{n}$, where $Z$ is the atomic number and $n$ is the orbit number.For a $He^{+}$ ion, the atomic number $Z = 2$.For the $1^{st}$ orbit $(n=1)$, the velocity is $v_1 = v_0 \frac{2}{1} = 2v_0$.For the $3^{rd}$ orbit $(n=3)$, the velocity is $v_3 = v_0 \frac{2}{3} = \frac{2}{3}v_0$.Therefore, the ratio $v_3 : v_1 = \frac{2}{3}v_0 : 2v_0 = \frac{1}{3} : 1 = 1 : 3$.

Consider an electron moving in the first Bohr orbit of a $He^{+}$ ion with a velocity $v_1$. If it is allowed to move in the third Bohr orbit with a velocity $v_3$, then indicate the correct $v_3: v_1$ ratio.

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