The wavelength will be minimum in the transitions of electrons from

The correct answer is Option (3) → n=2 to n=1

In a transition between Bohr levels the photon energy is \( \Delta E = hc/\lambda \), so the wavelength is smallest where the energy gap is largest. For hydrogen the level energies are \( E_n = -13.6/n^{2}\,\mathrm{eV} \).

    \( \displaystyle \Delta E = 13.6\left(\frac{1}{n_f^{2}}-\frac{1}{n_i^{2}}\right)\mathrm{eV} \)

    \( \displaystyle 4\to3:\ 13.6\left(\frac{1}{9}-\frac{1}{16}\right) \approx 0.66\,\mathrm{eV} \)

    \( \displaystyle 3\to2:\ 13.6\left(\frac{1}{4}-\frac{1}{9}\right) \approx 1.89\,\mathrm{eV} \)

    \( \displaystyle 2\to1:\ 13.6\left(1-\frac{1}{4}\right) = 10.2\,\mathrm{eV} \)

    \( \displaystyle 5\to4:\ 13.6\left(\frac{1}{16}-\frac{1}{25}\right) \approx 0.31\,\mathrm{eV} \)

The largest gap, \( 10.2\,\mathrm{eV} \), belongs to the transition \( n=2 \) to \( n=1 \), which therefore gives the minimum wavelength.

Note: The same question was also asked in CUET (UG) 2023 on 10-06-2023 (Slot 1) and on 27-05-2023 (Slot 3).