Question

The ratio of the wave lengths of the first line in the Lyman series of the spectrum of Hydrogen atom and the first line in the Balmer series of the spectrum of $H{e}^{+}$ is:

• A. 20/27
• B. 27/20
• C. 27/5
• D. 5/27

Answer 1

The correct option is C 27/5

For Lyman series

$n_1=1$ and $n_2=2$...

For $1^{st}$ line of Lyman series

$\Rightarrow \frac{1}{\lambda }=R{Z}^2(\frac{1}{(1{)}^2}-\frac{1}{(2{)}^2})=R{Z}^2\left(\frac{3}{4}\right)=\frac{3}{4}R$

For Balmer series, $n_1=2,n_2=3$

$\Rightarrow \frac{1}{\lambda }=R{Z}^2(\frac{1}{(2{)}^2}-\frac{1}{(3{)}^2})=R{Z}^2=\frac{5}{36}R$

Ratio= $\frac{3}{4}R/\frac{5}{36}R\Rightarrow \frac{3}{4}\times \frac{36}{5}=\frac{27}{5}$