In a certain electronic transition from the quantum level, 'n' to the ground state in atomic hydrogen in one or more steps, no line belonging to the Brackett series is observed. What wave numbers may be observed in the Balmer series? (R=Rydberg Constant)

No line belonging to Brackett series means n₂ $\le$ 4

Thus n₂ can be 4, 3, 2

Possible transitions are 4 → 3, 4 → 2, 4 → 1, 3 → 2, 3 → 1, 2 → 1

Lines belonging to Balmer series are 4 → 2 & 3 → 2

For the electronic transition 4 → 2,

 $\overline{\mathrm{v}}=\frac{1}{\mathrm{\lambda }}={\mathrm{R}}_{\mathrm{H}}{1}^2\left(\frac{1}{2^2}-\frac{1}{4^2}\right)$

   $=\frac{3{\mathrm{R}}_{\mathrm{H}}}{16}$

For the electronic transition 3 → 2,

$\overline{\mathrm{v}}=\frac{1}{\mathrm{\lambda }}={\mathrm{R}}_{\mathrm{H}}{1}^2\left(\frac{1}{2^2}-\frac{1}{3^2}\right)$

$=\frac{5{\mathrm{R}}_{\mathrm{H}}}{36}$