Answer to Question #85014 in Atomic and Nuclear Physics for akash singh

Question

For a hydrogen-like atom, give all possible spectral terms for n = 2 and n = 3.

Answer 1

The Rydberg formula for  wavelengths of spectral lines is as follows

$$\frac{1}{\lambda}=RZ^2\left(\frac{1}{n^2}-\frac{1}{n'^2}\right)$$

Here n is the lower energy level and n' is the upper energy level.

In the case n'=2 we get Balmer series:

$$n=3,4,5,\ldots, \infty$$

In the case n'=3 we get Paschen series:

$$n=4,5,6,\ldots, \infty$$