Question

Obtain approximately the ratio of the nuclear radii of the gold isotope ${}_{79}A{u}^{197}$ and the silver isotope ${}_{47}A{g}^{107}$.

Answer 1

Let $R_{Au}$ be the nuclear radius of the gold isotope and $R_{Ag}$ be the nuclear radius of the silver isotope.

We have the mass number of the gold, $A_{AU}$ is $197$ and the mass number of the silver, $A_{Ag}$ is $107$.

The ratio of the radii of te two nuclei is related with their ass number as:

$\frac{R_{Au}}{R_{Ag}}=(\frac{A_{A}u}{A_{A}g}{)}^{\frac{1}{3}}=(\frac{197}{107}{)}^{\frac{1}{3}}=1.2256$