An electron in the n = 7 level of the hydrogen atom relaxes to a lower energy level, emitting light of 397 nm. what is the value of n for the level to which the electron relaxed?

Explanation:

It is given that,

Initially, the electron is in n = 7 energy level. When it relaxes to a lower energy level, emitting light of 397 nm. We need to find the value of n for the level to which the electron relaxed. It can be calculate using the formula as :

R = Rydberg constant,

Solving above equation we get the value of final n is,

or

So, it will relax in the n = 2. Hence, this is the required solution.