(II) Estimate the binding energy of the third electron in...

(II) Estimate the binding energy of the third electron in lithium using Bohr theory. [Hint: This electron has $n=2$ and "sees" a net charge of approximately $+1 e . ]$ The measured value is 5.36 $\mathrm{eV} .$

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Key Concepts

Bohr Model

The Bohr model describes electrons moving in quantized circular orbits around the nucleus. It provides a formula for calculating the energy levels of an electron by taking into account factors such as the principal quantum number and effective nuclear charge, making it a useful approximation for estimating atomic binding energies.

Effective Nuclear Charge

Effective nuclear charge is the net positive charge experienced by an electron in a multi-electron atom, accounting for the shielding effects of inner electrons. In calculations using the Bohr model, replacing the actual nuclear charge with this effective value allows for more accurate predictions of electron energy levels in atoms beyond the simplest cases.

Principal Quantum Number

The principal quantum number, denoted as n, indicates the energy level and relative distance of an electron's orbit from the nucleus. In the Bohr theory, the energy of an electron is inversely proportional to the square of n, so a higher quantum number corresponds to less tightly bound electrons.

Binding Energy

Binding energy is the energy required to remove an electron from an atom. In the context of Bohr theory, it is determined by the quantized energy level of the electron and the effective nuclear charge it experiences, providing insight into the electron’s stability within the atom.

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