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Question

If velocity of an electron in 1st orbit of H atom is V, what will be the velocity in 3rd orbit of Li$$^{2+}$$ ?


A
V
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B
V3
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C
3V
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D
9V
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Solution

The correct option is A $$V$$
$$V$$ of H$$_2^{\oplus}$$ = $$\displaystyle\frac{2 \pi Ze^2}{nh} $$or V $$\alpha$$ $$\displaystyle\frac{Z}{n}$$
$$\therefore$$ V H$$_2^{\oplus}$$ $$\alpha$$  1  $$\space $$ (Z = 1, n = 1)
$$V$$ of Li$$^{2+}$$ $$\alpha$$ $$\displaystyle\frac{3}{3}$$ $$\alpha$$ 1 (Z = 3, n = 3)
Therefore, velocity of e$$^-$$ in the third orbit of Li$$^{2+}$$ is the same velocity of an e$$^-$$ in the first orbit of H atom

Chemistry

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