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Q.
If velocity of an electron is 1 st orbit of $H$ atom is $V$, what will be the velocity in $3 rd$ orbit of $Li ^{2+}$ ?
Structure of Atom
Solution:
$V_{ H _2}^{\oplus}=\frac{2 \pi Z e^2}{n h}$ or $V \propto \frac{Z}{n}$
$\therefore V_{ H _2}^{\oplus} \propto 1(Z=1, n=1)$
$V_{ Li ^{2+}} \propto \frac{Z}{n} \propto \frac{3}{3} \propto 1(Z=3, n=3)$
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, i.e., $V$