Match the electron transitions in a hydrogen atom (List I) with the corresponding energy of the emit

Question

Match the electron transitions in a hydrogen atom (List I) with the corresponding energy of the emitted photon in eV (List II). 
$\begin{aligned}
&	extbf{List I} && 	extbf{List II} \
	ext{(A)} \quad & n=2 	o n=1 \qquad\qquad & 	ext{(I)} \quad & 12.09 \mathrm{~eV} \
	ext{(B)} \quad & n=3 	o n=1 & 	ext{(II)} \quad & 10.2 \mathrm{~eV} \
	ext{(C)} \quad & n=4 	o n=1 & 	ext{(III)} \quad & 13.06 \mathrm{~eV} \
	ext{(D)} \quad & n=5 	o n=1 & 	ext{(IV)} \quad & 12.75 \mathrm{~eV}
\end{aligned}$ \Choose the correct match.

Professor PC Thomas Classes · Answer

(b) : The energy of a photon emitted during a transition to the ground state is $\Delta E = 13.6 \left(1 - \frac{1}{n^2}ight) \mathrm{~eV}$. For $n=2 	o 1$, $\Delta E = 13.6(3/4) = 10.2 \mathrm{~eV}$ (A $	o$ II). For $n=3 	o 1$, $\Delta E = 13.6(8/9) \approx 12.09 \mathrm{~eV}$ (B $	o$ I). For $n=4 	o 1$, $\Delta E = 13.6(15/16) \approx 12.75 \mathrm{~eV}$ (C $	o$ IV). For $n=5 	o 1$, $\Delta E = 13.6(24/25) \approx 13.06 \mathrm{~eV}$ (D $	o$ III).