An electron is in the ground state of the hydrogen-like ion Li²⁺. Using 13.6 eV as the magnitude of the hydrogen ground-state energy, if the binding energy of the Li²⁺ electron is approximately N eV, rounded to the nearest integer, find N.
Physics · Atomic Structure and X-rays · atomic structure and bohr atomic model
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Question

An electron is in the ground state of the hydrogen-like ion Li²⁺. Using 13.6 eV as the magnitude of the hydrogen ground-state energy, if the binding energy of the Li²⁺ electron is approximately N eV, rounded to the nearest integer, find N.

Physics · Atomic Structure and X-rays · atomic structure and bohr atomic model

G1 Physics · Accepted Answer

For a hydrogen-like ion, Eₙ = −13.6Z² ÷ n² eV. For Li²⁺ in the ground state: Z = 3, n = 1. Thus, E₁ = −13.6×3² = −13.6×9 = −122.4 eV. Binding energy is the positive energy required to remove the electron to infinity: BE = 122.4 eV. Rounded to the nearest integer, N = 122.