Can someone show me how to solve these problems? (help quickly please!)?

Question

calculate the energy corresponding to the n=3 electronic state in the Bohr hydrogen atom


calculate the energy change correspondin the excitation of an alectron from the n=1 to the n=3 electronic state in the hydrogen atom


can you show me the work too so i understand it?

Answer 1

In Bohr model, the energy is the summation of the kinetic energy and potential energy of the only electron rotating around the nuclear: E = 0.5mv^2 - ke^2/r = -ke^2/2r. Introduce angular momentum, the energy can be further written as:
E_n = -13.606 eV/n^2, where eV is the electron voltage (1V*e). For n = 3, E_3 = -1.51 eV.
The transition energy is then E_3 - E_1 = -1.51 + 13.61 = 12.1eV.
You simply need to remember: E_n = -13.606 eV/n^2.