(a)
$E_{n} = \frac{13.6}{n^{2}}eV$
$E_{3} - E_{2} = 13.6\left( \frac{1}{(2)^{2}} - \frac{1}{(3)^{2}} \right)eV$
$E_{3} - E_{2} = 13.6\ \left( \frac{1}{4} - \frac{1}{9} \right)eV$
$E_{3} - E_{2} = 13.6 \times \left( \frac{5}{36} \right)eV$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = 1.9\ eV$