Explanation

(b) Least energy of photon of Balmer series is obtained when an electron jumps to 2nd orbit from 3rd orbit.
$E = E_{3} - E_{2} = \left\lbrack \frac{- 13.6}{3^{2}} - \left( \frac{- 13.6}{2^{2}} \right) \right\rbrack eV$
$= 13.6\left\lbrack \frac{1}{4} - \frac{1}{9} \right\rbrack = \frac{13.6 \times 5}{36}eV$
$= 1.89\ eV$