In a mixture of $\mathrm{H}-\mathrm{He}^{+}$gas ( $\mathrm{He}^{+}$is singly ionized $\mathrm{He}$ 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.
$1.$ The quantum number $\mathrm{n}$ of the state finally populated in $\mathrm{He}^{+}$ions is
$(A)$ $2$ $(B)$ $3$ $(C)$ $4$ $(D)$ $5$
$2.$ The wavelength of light emitted in the visible region by $\mathrm{He}^{+}$ions after collisions with $\mathrm{H}$ atoms is
$(A)$ $6.5 \times 10^{-7} \mathrm{~m}$ $(B)$ $5.6 \times 10^{-7} \mathrm{~m}$
$(C)$ $4.8 \times 10^{-7} \mathrm{~m}$ $(D)$ $4.0 \times 10^{-7} \mathrm{~m}$
$3.$ The ratio of the kinetic energy of the $\mathrm{n}=2$ electron for the $\mathrm{H}$ atom to that of $\mathrm{He}^{+}$ion is
$(A)$ $\frac{1}{4}$ $(B)$ $\frac{1}{2}$ $(C)$ $1$ $(D)$ $2$
Give the answer question $1,2$ and $3.$
