Final answer:
The minimum energy (Emin) a photon must have to free an electron from the twenty-second energy level of a hydrogen atom is 0.0281 eV.
Step-by-step explanation:
To determine the energy (in eV) that a photon must have to free an electron in the twenty-second energy level (n=22) of a hydrogen atom, we use the formula for the energy of the electron in a given energy level: En = -13.6 eV/n². Inserting n=22, we get E22 = -13.6 eV / 22² = -13.6 eV / 484 = -0.0281 eV. The energy needed to ionize the hydrogen atom (Emin) when the electron is in the twenty-second energy level is the difference between the energy at infinity (where the electron is free) and the energy at that level, which is 0 eV - (-0.0281 eV) = 0.0281 eV.
The minimum energy (Emin) a photon must have to free an electron from the twenty-second energy level of a hydrogen atom is 0.0281 eV. The energy needed to ionize the hydrogen atom (Emin) when the electron is in the twenty-second energy level is the difference between the energy at infinity (where the electron is free) and the energy at that level, which is 0 eV - (-0.0281 eV) = 0.0281 eV.