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Answer :
The energy required to excite an electron in a Li2+ ion from the first Bohr orbit to the third orbit can be determined using the Bohr model formula. Considering the atomic number of lithium and the Rydberg constant, the energy required is 122.4 eV, corresponding to option D).
The student is asking about the energy required for the excitation of an electron from the first to the third orbit in a doubly ionized lithium ion (Li2+). In the context of the Bohr model, the energy levels of the electrons in a Li2+ ion are quantized and can be calculated using the formula E = -Z2R/n², where E is the energy, Z is the atomic number, R is the Rydberg constant (13.6 eV for hydrogen-like species), and n is the principal quantum number of the orbit.
To determine the energy required to excite the electron from n=1 to n=3, we first calculate the energies of both states and then find the difference. The energy of an electron in the first orbit of Li²+ is E1 = -Z2R and in the third orbit is E3 = -Z2R/9. The energy required for the excitation is ΔE = E3 - E1.
Substituting Z=3 (for lithium) and R=13.6 eV, we find the energy required for excitation is ΔE = 122.4 eV, which corresponds to option D).
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