If the outer electron in lithium moves in the n=2 Bohr...

If the outer electron in lithium moves in the $n=2$ Bohr orbit, the effective nuclear charge would be $Z_{\text {eff }} e=1 e,$ and the energy of the electron would be $-13.6 \mathrm{eV} / 2^{2}=-3.4 \mathrm{eV}$. However, the ionization energy of lithium is $5.39 \mathrm{eV},$ not $3.4 \mathrm{eV}$ Use this fact to calculate the effective nuclear charge $Z_{\text {eff }}$ seen by the outer electron in lithium. Assume that $r=4 a_{0}$ for the outer electron.

Key Concepts

Shielding Effect

The shielding effect occurs when inner electrons reduce the full nuclear charge experienced by outer electrons through electron-electron repulsion. This reduction in effective nuclear charge modifies the energy levels and the spatial distribution of electron orbits. Understanding shielding is crucial when calculating properties such as ionization energy and analyzing deviations from simple models that assume a bare nucleus.

Bohr Model

The Bohr model introduces the idea that electrons occupy quantized orbits around the nucleus, with their energies depending on the principal quantum number (n) and the square of the nuclear charge (or effective nuclear charge in multi-electron atoms). This model, though limited to simpler hydrogen-like systems, establishes the basic relationship between electron energy levels and the forces acting within an atom.

Effective Nuclear Charge

Effective nuclear charge (Z?ff) represents the net positive charge experienced by an electron in a multi-electron atom after accounting for the repulsion from other electrons. This concept explains why electrons, particularly those in outer orbits, feel a nuclear attraction that is significantly reduced from the full nuclear charge, leading to adjustments in predicted energy levels and other atomic properties.

Ionization Energy

Ionization energy is the energy required to remove an electron completely from an atom or ion. It provides a measure of the binding energy of an electron and is directly influenced by the effective nuclear charge experienced by that electron. A higher Z?ff generally corresponds to a greater ionization energy, indicating a stronger attraction between the nucleus and the electron.

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