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 $n =2$
$\frac{1}{\lambda_{1}}=R\left(\frac{1}{2^{2}}-\frac{1}{3^{2}}\right) =R.\frac{5}{9\times4}$
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, $\frac{\lambda_{2}}{\lambda_{1}}=\frac{5}{9\times4}\times\frac{9\times25 }{16}$
or $\lambda_{2} =\frac{125}{64}\lambda_{1} $