# How do I calculate the change in energy of an electron transition?

What are the $\Delta E$'s of the transitions of an electron from $n=5$ to $n=1$ and from $n=5$ to $n=2$ in a Bohr hydrogen atom? The wavelength of the first electron transition is $\lambda_1=409~\mathrm{nm}$ and the other electron transition $\lambda_2=1091~\mathrm{nm}$.

How can I solve this using those two given wavelengths?

The energy of light at a given frequency $\nu$ is $$E = h\nu\; ,$$ where $h$ is Planck's constant. The frequency of light is directly related to the wavelength $\lambda$ and the speed of light $c$ via $$c = \nu\lambda\; .$$
Combining these two equations we get $$E = \frac{hc}{\lambda}\; ,$$ with which you should be able to calculate the $\Delta E$ values for the transitions.