Hydrogen atom energy: E_n = -13.6 eV / n^2. What is the energy of the electron in the n = 2 state? What is the ionization energy from the ground state?

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Multiple Choice

Hydrogen atom energy: E_n = -13.6 eV / n^2. What is the energy of the electron in the n = 2 state? What is the ionization energy from the ground state?

Explanation:
In hydrogen, bound-state energies are negative and follow E_n = -13.6 eV / n^2. For the state with n = 2, E_2 = -13.6 eV / 4 = -3.4 eV, so the electron in that level has energy -3.4 eV. The ionization energy from the ground state is the energy required to remove the electron completely, i.e., raise the energy from E_1 = -13.6 eV to 0. The needed amount is 0 - (-13.6) = 13.6 eV. So the energy of the electron in the n = 2 state is -3.4 eV, and the ionization energy from the ground state is 13.6 eV.

In hydrogen, bound-state energies are negative and follow E_n = -13.6 eV / n^2. For the state with n = 2, E_2 = -13.6 eV / 4 = -3.4 eV, so the electron in that level has energy -3.4 eV.

The ionization energy from the ground state is the energy required to remove the electron completely, i.e., raise the energy from E_1 = -13.6 eV to 0. The needed amount is 0 - (-13.6) = 13.6 eV.

So the energy of the electron in the n = 2 state is -3.4 eV, and the ionization energy from the ground state is 13.6 eV.

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