Question

What are the wavelengths of spectral lines in the Balmer

series with $n=6,8$and $10$?

Short answer

The wavelengths of spectral lines in the Balmer

series with n $=$$6$, $8$and $10$are $410.31$(nm) ,$389.03$(nm) and$379.92$(nm) respectively..

Step-by-step solution

Given information

We can use the formula for the balmer series :

$\frac{1}{2^2}-\frac{1}{n^2}=\frac{91.18\left(nm\right)}{\lambda }(n=3,4,5,6.....)$

$$\begin{gathered} \lambda =\frac{91.18\left(nm\right)}{\frac{1}{2^2}-\frac{1}{n^2}} \\ {\lambda }_6=\frac{91.18\left(nm\right)}{\frac{1}{2^2}-\frac{1}{6^2}}(substituten=6) \\ {\lambda }_6=410.31nm \\ {\lambda }_8=\frac{91.18\left(nm\right)}{\frac{1}{2^2}-\frac{1}{8^2}}(substituten=8) \\ {\lambda }_8=389.01nm \\ {\lambda }_{10}=\frac{91.18\left(nm\right)}{\frac{1}{2^2}-\frac{1}{{10}^2}}(substituten=10) \\ {\lambda }_{10}=379.92nm \end{gathered}$$