Final answer:
A hydrogen atom requires 0.544 eV of energy to be ionized when its electron is in the n = 5 orbit. This is calculated using the Bohr model formula for energy levels of hydrogen atoms.
Step-by-step explanation:
The question pertains to the amount of energy required to ionize a hydrogen atom, specifically when the electron is in the n = 5 orbit. According to the Bohr model of the hydrogen atom, the energy required to ionize an electron from any given state can be calculated using the energy level formula for hydrogen, En = (-13.6 eV/n²). Thus, for n = 5, the energy of the state is E5 = (-13.6 eV/5²) = -0.544 eV. The ionization energy is the difference in energy between that level and the energy of a free electron, which is 0 eV.
To ionize the electron from n = 5, we need to provide enough energy to bring the electron from -0.544 eV to 0 eV. This can be given by the difference, which is 0 eV - (-0.544 eV) = 0.544 eV. Therefore, 0.544 eV of energy is required to ionize a hydrogen atom when the electron is in the n = 5 orbit.
The energy required to ionize a hydrogen atom can be calculated using the formula:
E = (13.6 eV) / n^2
Here, n represents the principal quantum number of the electron's orbit. In this case, the electron occupies the n = 5 orbit.
Substituting the value of n = 5 into the formula, we get:
E = (13.6 eV) / (5^2) = 0.544 eV
Therefore, the energy required to ionize a hydrogen atom when the electron occupies the n = 5 orbit is 0.544 eV.