Final answer:
To ionize a hydrogen atom from its n = 3 state, 12.09 eV of energy is required. This value is derived from subtracting the energy at n = 3 from the ionization energy from the ground state.
Step-by-step explanation:
The energy required to ionize a hydrogen atom when it is in the n = 3 state can be calculated using the formula En = -13.6 eV/n². For n = 3, we get E3 = -13.6 eV/9 = -1.51 eV. Since ionization requires the energy to go from the electron's current energy level to zero, the required ionization energy is 13.6 eV (the energy required to ionize from the ground state) minus the energy of the current state.
Therefore, the ionization energy from n = 3 is 13.6 eV - 1.51 eV, which equals 12.09 eV.