Some Properties of Atoms — Question 1

Question 1

Ion charge and isotope labels encode independent counts

An ion is written $^{57}_{26}\mathrm{Fe}^{3+}$. Use $q=(Z-N_e)e$ and $A=Z+N_n$, where $N_e$ and $N_n$ count electrons and neutrons.

1. Find all three particle counts.

2. One electron is captured without changing the nucleus. Write the new ion and determine the fractional change in its net charge.

Question 1 - Solution

Ion charge and isotope labels encode independent counts

(a) Method and calculation

$$Z=26,\quad N_n=A-Z=57-26=\boxed{31}.$$$$N_e=Z-q/e=26-3=\boxed{23};\qquad N_p=26.$$

(b) Interpretation and further calculation

$$N_e\prime=24\Rightarrow q\prime=(26-24)e=2e\Rightarrow\boxed{^{57}_{26}\mathrm{Fe}^{2+}}.$$$$\boxed{(q\prime-q)/q=(2e-3e)/(3e)=-1/3}.$$

Physical check

Ionization changes electron count, not the atomic number or isotope. The net charge decreases even though the number of negatively charged particles increases.