Using E_n = -13.6 eV / n^2, what is the energy of the n = 2 level for a hydrogen-like atom?

Using E_n = -13.6 eV / n^2, what is the energy of the n = 2 level for a hydrogen-like atom?

• A. -3.4 eV
• B. -1.35 eV
• C. -6.8 eV
• D. -13.6 eV

Answer: (A)

In hydrogen-like atoms, bound-state energies are quantized and follow E_n = -13.6 eV / n^2. The energies are negative and become less negative (approach zero) as n increases. For n = 2, E_2 = -13.6 eV / (2^2) = -13.6 / 4 = -3.4 eV. This is the energy of the first excited level. The ground state is -13.6 eV, and higher levels follow the same 1/n^2 scaling (e.g., n = 3 gives about -1.51 eV, n = 4 about -0.85 eV). The other numbers don’t correspond to any integer n in this formula.

In hydrogen-like atoms, bound-state energies are quantized and follow E_n = -13.6 eV / n^2. The energies are negative and become less negative (approach zero) as n increases. For n = 2, E_2 = -13.6 eV / (2^2) = -13.6 / 4 = -3.4 eV. This is the energy of the first excited level. The ground state is -13.6 eV, and higher levels follow the same 1/n^2 scaling (e.g., n = 3 gives about -1.51 eV, n = 4 about -0.85 eV). The other numbers don’t correspond to any integer n in this formula.