Question

The wave length of the first Balmer line caused by a transition from the $n=3$ level to the $n=2$ level in hydrogen is ${\lambda }_1$ The wave length of the line caused by an electronic transition from $n=5$ to $n=3$ is

• A. $\frac{375}{168}{\lambda }_1$
• B. $\frac{125}{64}{\lambda }_1$
• C. $\frac{64}{125}{\lambda }_1$
• D. $\frac{128}{375}{\lambda }_1$

Answer 1

Answer: (B)

Using Balmer’s formula,
we have For transition $n=3$ to $n=2$
$\frac{1}{{\lambda }_1}=R\left(\frac{1}{2^2}-\frac{1}{3^2}\right)=R.\frac{5}{9\times 4}$
and for transition $n=5$ to $n=3,$
$\frac{1}{{\lambda }_1}=R\left(\frac{1}{3^2}-\frac{1}{5^2}\right)=R.\frac{16}{9\times 25}$
So, $\frac{{\lambda }_2}{{\lambda }_1}=\frac{5}{9\times 4}\times \frac{9\times 25}{16}$
or ${\lambda }_2=\frac{125}{64}{\lambda }_1$