JEE Main · 2021 · 24 Feb 2021 · Shift 2 · Modern Physics

The frequency emitted follows from $h\nu =E_i-E_f$, which for hydrogen gives

The bracket equals $\frac{3}{4}$ for the jump from $n=2$ to $n=1$, $\frac{5}{36}$ for $n=3$ to $n=2$, $\frac{7}{144}$ for $n=4$ to $n=3$ and $\frac{9}{400}$ for $n=5$ to $n=4$. Energy levels crowd together as $n$ grows, so the widest gap is always the lowest one, and the frequency is maximum for the transition from $n=2$ to $n=1$.