Question

A hydrogen-like atom has ground state binding energy 122.4eV. Then :

(a). its atomic number is 3
(b). an electron of 90eV can excite it to a higher state
(c). an 80eV electron cannot excite it to a higher state
(d). an electron of 8.2eV and a photon of 91.8eV are emitted when a 100eV electron interacts with it


A. Its atomic number is 3
B. a photon of 90 eV can excite it to a higher state
C. a 80 eV photon cannot excite it to a higher state
D. to excite an e− minimum 91.8 eV photon is required

Answer 1

The minimum energy required to excite an electron in a hydrogen-like atom from the ground state to an excited state is determined by the difference in energy levels. For the fifth excited state, the necessary photon is at least 122.022 eV, not the 91.8 eV indicated by the student.

Step-by-step explanation:

The question is about the energy required to excite an electron in a hydrogen-like atom from the ground state to an excited state. The ground state binding energy for hydrogen is 13.6 eV, which is the energy needed to ionize the atom by freeing the electron from its ground state. Given that this hydrogen-like atom has a ground state binding energy of 122.4 eV, the ionization energy for its electron will be higher than that of hydrogen.

When the atom is in the fifth excited state (n = 6), the ionization energy required is 36 times less than from the ground state, which implies the energy required from the fifth excited state is 122.4 eV / 36 = 3.4 eV. As the electron is at a bound state with energy -0.378 eV in the fifth excited state, the energy required to bring the electron to that state from the ground state is the difference between the ground state energy and the excited state energy, which is 122.4 eV - 0.378 eV = 122.022 eV. Therefore, the minimum energy photon required to achieve excitation to the fifth state must be at least 122.022 eV. However, the student states that a minimum 91.8 eV photon is required to excite the electron, which suggests that this excitation energy does not correspond to the fifth excited state but perhaps to a lower excited state.