Question

Whats the absorption energy of a photon when moving from the first state to the fifth state?

Answer 1

`13.056eV`

Explanation:

I will assume you mean for hydrogen. To find the change in energy, we need to use the Rydberg Equation, which is:

`DeltaE=Z^2R(1/n_f^2-1/n_i^2)`

It is given that `n_i`, the initial state is 1 and `n_f`, the final state is 5. Z depends on the number of protons in the atom, which for hydrogen is 1. I will assume the question is for a hydrogen atom. R is the Rydberg constant, which is -13.6 eV.
Plugging in the numbers:

`DeltaE=1^2*-13.6eV(1/5^2-1/1^2)`
`DeltaE=13.056eV`