Question

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

• A. $V$
• B. $\frac{V}{3}$
• C. $3V$
• D. $9V$

Answer 1

Answer: (A)

$V_{H_2}^{\oplus }=\frac{2\pi Z{e}^2}{nh}$ or $V\propto \frac{Z}{n}$
$\therefore V_{H_2}^{\oplus }\propto 1(Z=1,n=1)$
$V_{L{i}^{2+}}\propto \frac{Z}{n}\propto \frac{3}{3}\propto 1(Z=3,n=3)$
Therefore, velocity of $e^{-}$in the third orbit of $L{i}^{2+}$ is the same velocity of an $e^{-}$in the first orbit of $H$ atom, i.e., $V$