Find the radii of the { }^{238} U \text { and }{ }^{4} He nuclei and then determine the ratio of those radii.
Strategy We use Equation (12.2) to determine the radii and then the ratio for the two nuclei.
R=r_{0} A^{1 / 3} (12.2)
Chapter 12
Q. 12.3
Step-by-Step
Verified Solution
\begin{aligned}&R\left({ }^{238} U \right)=(1.2 fm )(238)^{1 / 3}=7.4 fm \\&R\left({ }^{4} He \right)=(1.2 fm )(4)^{1 / 3}=1.9 fm\end{aligned}
The ratio is
\frac{R\left({ }^{238} U \right)}{R\left({ }^{4} He \right)}=\frac{7.4 fm }{1.9 fm }=3.9
Even though { }^{238} U has 60 times the number of nucleons of { }^{4} He, its radius is only four times greater.