Question

The velocity of electron moving in $3^{rd}$ orbit of $H{e}^{+}$ is $v$. The velocity of electron moving in $2^{nd}$ orbit of $L{i}^{+2}$ is:

• A. $\frac{9}{4}v$
• B. $\frac{4}{9}v$
• C. $v$
• D. None of these

Answer 1

Answer: (A)

$\frac{9}{4}v$

$V_n=\left(\frac{c}{137}\right)\frac{Z}{n}$
$V_n\alpha \frac{Z}{n}$
$3^{rd}$ orbit of $H{e}^{+}$
$V=\left(\frac{c}{137}\right)\left(\frac{2}{3}\right)⟹\frac{c}{137}=\frac{3V}{2}$
$2^{nd}$ orbit of $L{i}^{2+}$
$V_{Li}=\left(\frac{c}{137}\right)\left(\frac{3}{2}\right)$
$=\left(\frac{3V}{2}\right)\left(\frac{3}{2}\right)$
$=\left(\frac{9V}{4}\right)$