Question

If the velocity of electron in third orbit of $H{e}^{+}$ ion is ${}^{\prime }{x}^{\prime }$, calculate velocity of electron in second orbit of $L{i}^{2+}$ ion.

• A. $\frac{9}{4}x$
• B. $\frac{4}{9}x$
• C. $\frac{7}{4}x$
• D. $\frac{4}{7}x$

Answer 1

The correct option is A $\frac{9}{4}x$

We know,
$\text{Velocity},\left(v\right)=2.18\times {10}^6\frac{Z}{n}\text{m/s}$
For, $H{e}^{+},z=2\text{and}n=3$
$\therefore 2.18\times {10}^6\times \frac{2}{3}=x....\left(i\right)$
For, $L{i}^{2+},z=3\text{and}n=2$
$\therefore 2.18\times {10}^6\times \frac{3}{2}=V....\left(ii\right)$
From equation, $\frac{\left(ii\right)}{\left(i\right)}$
$\frac{V}{x}=\frac{3}{2}\times \frac{3}{2}=\frac{9}{4}x$