Final answer:
The ionization energy required to ionize a hydrogen atom in its first excited state (n=2) is 3.4 eV.
Step-by-step explanation:
To compute the ionization energy of a hydrogen atom in its first excited state, we need to understand the energy levels of the atom. The ground state energy level of hydrogen is -13.6 eV, and the energy levels of higher states are given by En = -13.6 eV/n², where n is the principal quantum number representing the energy level.
For the first excited state of hydrogen, n=2. Thus, the energy for this level is E2 = -13.6 eV/2² = -13.6 eV/4 = -3.4 eV. To ionize the hydrogen atom from this state, we must provide enough energy to raise the electron from -3.4 eV to 0 eV, the ionization energy threshold.
Therefore, the ionization energy required for a hydrogen atom in the n=2 state is 3.4 eV.