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

Question

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

Quizplus · Accepted Answer

The radius of the electron orbit in a hydrogen-like atom (an atom with only one electron) is given by $R_n = n^2 \frac{R}{Z}$ for the nth orbit, where R is the radius of the ground state electron orbit in atomic hydrogen, and Z is the atomic number. Since we are considering the ground state (n=1) of an ionized atom with Z protons and only one electron, the radius of the shell of the remaining electron is $R / Z$.

An Ionized Atom Having Z Protons Has Had All but One