Final answer:
To ionize a hydrogen atom with an electron in the n=2 energy level, 3.4 eV of energy is required, as calculated by the difference between the energy of an electron in the n=2 state (-3.4 eV) and the energy of a free electron (0 eV).
Step-by-step explanation:
The question asks how much energy is required to ionize a hydrogen atom containing an electron in the n=2 level. Ionization energy refers to the energy needed to remove an electron from an atom to form a cation. The energy levels of a hydrogen atom's electrons are quantized and can be described by the formula En = (-13.6 eV/n²). The ground state, or the lowest energy level, is n=1, which has an energy of -13.6 eV. To ionize a hydrogen atom from the ground state, 13.6 eV of energy is required to bring the electron from -13.6 eV to 0 eV. However, if the electron is in the n=2 level, its energy level is En = (-13.6 eV/2²) = -3.4 eV. This means the electron is already at a higher potential than in the ground state, and therefore requires less energy to ionize. To find the ionization energy from the n=2 level, we need to calculate the difference between the energy of the n=2 state and the energy of a free electron (0 eV).
To ionize the hydrogen atom from the n=2 level, the energy required is (0 eV) - (-3.4 eV) = 3.4 eV. Thus, the correct answer is c. 3.4 eV.