Question:
Radiation coming from transitions $n=2$ to $n=1$ of hydrogen atoms fall on $\mathrm{He}^{+}$ions in $n=1$ and $n=2$ states. The possible transition of helium ions as they absorb energy from the radiation is :
Correct Option: , 4
Solution:
(4) Energy released by hydrogen atom for transition $n=2$ to $n=1$
$\therefore \Delta E_{1}=13.6 \times\left(\frac{1}{1^{2}}-\frac{1}{2^{2}}\right)=\frac{3}{4} \times 13.6 \mathrm{eV}=10.2 \mathrm{eV}$
This energy is absorbed by $\mathrm{He}^{+}$ion in transition from $n$ $=2$ to $n=n_{1}$ (say)
$\therefore \Delta E_{2}=13.6 \times 4 \times\left(\frac{1}{4}-\frac{1}{n_{1}^{2}}\right)=10.2 \mathrm{eV}$
$\Rightarrow \mathrm{n}_{1}=4$
So, possible transition is $\mathrm{n}=2 \rightarrow \mathrm{n}=4$