Final answer:
The energy required to ionize hydrogen in the ground state is about 13.6 eV, and for the excited state with n = 3, it is 12.09 eV.
Step-by-step explanation:
The energy required to ionize a hydrogen atom in the ground state (n = 1) is known as the ionization energy and is approximately 13.6 eV. This is the energy necessary to remove the single electron from the hydrogen nucleus (proton) when the electron is in its lowest energy level. Concerning part (b) of the question, when the hydrogen atom is in an excited state such as n = 3, the energy required to ionize it is lower since the electron is already at a higher energy level compared to the ground state.
Answering the specific query concerning n = 3, using the Rydberg formula for the energy levels of hydrogen, En = -13.6 eV/n2, we can calculate the energy required to ionize from the third state:
Ei (ionization from n = 3) = 13.6 eV - E3 = 13.6 eV - (-13.6 eV/32) = 13.6 eV - 1.51 eV = 12.09 eV.
Similarly, if the student needs to find this energy for any other state like n = 4 or if 0.850 eV can ionize the atom, they would have to use the same formula to determine the energy of the specific energy state and subtract it from the ionization energy to find the energy required to ionize from that specific excited state.