उत्तर: (32)

समाधान:

$E=-13.6 z^{2}\left(\frac{1}{n _i^{2}}-\frac{1}{n _f^{2}}\right)$

$E=C\left(\frac{1}{n _f^{2}}-\frac{1}{n _i^{2}}\right)$

$h v=C\left[\frac{1}{n _f^{2}}-\frac{1}{n _i^{2}}\right]$

$\frac{v _1}{v _2}=\frac{\left[\frac{1}{n _f^{2}}-\frac{1}{n _i^{2}}\right] _{2-1}}{\left[\frac{1}{n _f^{2}}-\frac{1}{n _i^{2}}\right] _{3-1}}$

$=\frac{\left[\frac{1}{1}-\frac{1}{4}\right]}{\left[\frac{1}{1}-\frac{1}{9}\right]}=\frac{3 / 4}{8 / 9}$

$=\frac{3}{4} \times \frac{9}{8}$

$\frac{v _1}{v _2}=\frac{27}{32}$

$v _2=\frac{32}{27} v _1=\frac{32}{27} \times 3 \times 10^{15} Hz=\frac{32}{9} \times 10^{15} Hz$