Take the potential energy of a hydrogen atom to be zero for infinite separation of the electron and proton.Then the ground state energy of a hydrogen atom is -13.6 eV.When the electron is in the first excited state its excitation energy (the difference between the energy of the state and that of the ground state)is:

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The energy levels of a hydrogen atom are given by the formula E_n = -13.6 eV/n^2. For the ground state (n=1), the energy is -13.6 eV. For the first excited state (n=2), the energy is -13.6 eV/4 = -3.4 eV. The excitation energy is the difference between these two energies: -3.4 eV - (-13.6 eV) = 10.2 eV.

Take the Potential Energy of a Hydrogen Atom to Be