Question

What are the wavelengths of spectral lines in the Balmer series with $n=6,8,and10$?

Short answer

The wavelengths with$n=6,8,10$ are$410.31nm,389.03nmand379.92nm$respectively.

Step-by-step solution

Given information

We need to find the wavelengths of spectral lines in the Balmer series with $n=6,8,10$.

Explanation

Now the Rydberg formula for Balmer series is

$$\begin{gathered} \frac{1}{2^2}-\frac{1}{n^2}=\frac{91.18\left(nm\right)}{\lambda } \\ \lambda =\frac{91.18\left(nm\right)}{\frac{1}{2^2}-\frac{1}{n^2}} \end{gathered}$$

This is equation (1)

Now on substituting n value we get-

$For$$n=6$

$$\begin{gathered} {\lambda }_6=\frac{91.18\left(nm\right)}{{\displaystyle \frac{1}{2^2}}-{\displaystyle \frac{1}{6^2}}} \\ {\lambda }_6=410.31nm \\ Forn=8, \\ {\lambda }_8=\frac{91.18\left(nm\right)}{{\displaystyle \frac{1}{2^2}-\frac{1}{8^2}}} \\ {\lambda }_8=389.03nm \\ Forn=10, \\ {\lambda }_{10}=\frac{91.18\left(nm\right)}{{\displaystyle \frac{1}{2^2}-\frac{1}{{10}^2}}} \\ {\lambda }_{10}=379.92nm \end{gathered}$$