The electron in a hydrogen atom rises from its n = 1 state to n = 4 state by absorbing energy. The energy of the electron in the n = 1 state is -13.6 eV. How much energy is absorbed by the electron in transition?

12.75 eV

Energy of electron in n= 4 is $ E_f = \frac{-13.6}{4^2} = -0.85eV$

$E_i = -13.6 eV$

$ \Delta E = 13.6 - 0.85 = 12.75 eV$