Determine the energy of a hydrogen atom in the first excited state if the potential energy is taken to be zero in the ground state.

Step-by-step solution

The total energy of an electron in the n^ th orbit of a hydrogen atom is given by E_n = - 13.6 n^2 eV . The potential energy is twice the total energy, so U_n = 2E_n = - 27.2 n^2 eV . In the ground state ( n=1 ), the standard potential energy is U₁ = -27.2 eV . If the potential energy in the ground state is taken to be zero, the reference level of potential energy is shifted by +27.2 eV . Since kinetic energy remains unaffected by the choice of reference, the total energy of every state also increases by +27.2 eV .