Paragraph: In a mixture of $\mathrm{H}-\mathrm{H}^{+}$gas $\left(\mathrm{He}^{+}\right.$is singly ionised…
Paragraph:
In a mixture of $\mathrm{H}-\mathrm{H}^{+}$gas $\left(\mathrm{He}^{+}\right.$is singly ionised $\mathrm{He}$ atom), $\mathrm{H}$ atoms and $\mathrm{He}^{+}$ions are excited to their respective first excited states. Subsequently, $\mathrm{H}$ atoms transfer their total excitation energy to $\mathrm{He}^{+}$ions (by collisions). Assume that the Bohr model of atom is exactly valid.Question:
The ratio of the kinetic energy of the $n=2$ electron for the $\mathrm{H}$ atom to that of $\mathrm{He}^{+}$ ion is
$\frac{1}{4}$
$\frac{1}{2}$
1
2
Solution
Kinetic energy $K \propto Z^2$
$
\frac{K_H}{K_{\mathrm{He}^{+}}}=\left(\frac{1}{2}\right)^2=\frac{1}{4}
$
$\therefore$ correct option is (a).
!