Question

Electron in hydrogen akin first Jumps from third excited state to second excited state and then from second excited to the first excited state The ratio of the wavelengths ${\lambda }_1:{\lambda }_2$ emitted in the two cases is

• A. $\frac{7}{5}$
• B. $\frac{27}{20}$
• C. $\frac{27}{5}$
• D. $\frac{20}{7}$

Answer 1

The correct option is D $\frac{20}{7}$

Here wave length ${\lambda }_1$ for wave length${\lambda }_2$

$n_{1}4and{n}_2=3$ $n_1=3n_2=2$

$\therefore \frac{hc}{\lambda }=-13.6\left[\frac{1}{n_2^2-\frac{1}{n_1^2}}\right]$

so for ${\lambda }_1$

$\frac{hc}{{\lambda }_1}=-13.6[\frac{1}{h^2}-\frac{1}{3^2}]=-13.6\left[\frac{7}{144}\right]------\left(1\right)$

for ${\lambda }_2=-13.6[\frac{1}{3^2}-\frac{1}{2^2}]$

$=-13.6\left[\frac{5}{36}\right]------\left(2\right)$

$\therefore \frac{{\lambda }_1}{{\lambda }_2}=\frac{20}{7}$

(1)

(2)

$\therefore \frac{{\lambda }_1}{{\lambda }_2}=\frac{-13.6\left[\frac{7}{144}\right]}{-13.6\left[\frac{5}{36}\right]}=\frac{20}{7}$