An ionized atom having $Z$ protons has had all but one of its electrons removed. If $E$ is the total energy of the ground state electron in atomic hydrogen, then what is the total energy of the remaining electron in the ionized atom?
A) $E / Z ^ { 2 }$
B) $E$
C) $Z E$
D) $E / Z$
E) $Z ^ { 2 } E$

Question

Quizplus · Accepted Answer

The total energy of the remaining electron in the ionized atom scales with the square of the nuclear charge ($Z$), hence $Z^2E$. This is because the energy levels in a hydrogen-like atom are given by $E_n = -\frac{13.6 \text{ eV}}{n^2}Z^2$ for the nth energy level, and for the ground state ($n=1$), this simplifies to $E = -13.6 \text{ eV} \cdot Z^2$, indicating that the energy scales as $Z^2$.

An Ionized Atom Having ZZZ Protons Has Had All but One of Its Electrons Removed

An Ionized Atom Having $Z$ Protons Has Had All but One of Its Electrons Removed