Amonochromatic laser is exciting hydrogen atoms from the n=2 state to the n=5 state. part a what is the wavelength λ of the laser?

The energy levels of the hydrogen atom are given by

where n is the level number.

In order to make transition from n=2 state to n=5 state, the electron should acquire an energy equal to the difference between the two energy levels:


Keeping in mind that , we can convert this energy in Joules


This is the energy the photons of the laser should have in order to excite electrons from n=2 state to n=5 state. Their frequency can be found by using

where h is the Planck constant and f is the photon frequency. Re-arranging it, we find


and finally we can use the relationship between frequency, wavelength and speed of light which holds for photons, in order to find their wavelength:

and this is the laser wavelenghth.