Obtain approximately the ratio of the nuclear radii of the gold isotope
Question:

Obtain approximately the ratio of the nuclear radii of the gold isotope ${ }_{79}^{197} \mathrm{Au}$ and the silver isotope ${ }_{47}^{107} \mathrm{Ag}$.

Solution:

Nuclear radius of the gold isotope $_{79} \mathrm{Au}^{197}=R_{\mathrm{Au}}$

Nuclear radius of the silver isotope ${ }_{47} \mathrm{Ag}^{107}=R_{\mathrm{Ag}}$

Mass number of gold, AAu = 197

Mass number of silver, AAg = 107

The ratio of the radii of the two nuclei is related with their mass numbers as:

$\frac{R_{\mathrm{Au}}}{R_{\mathrm{Ag}}}=\left(\frac{R_{\mathrm{Au}}}{R_{\mathrm{Ag}}}\right)^{\frac{1}{3}}$

$=\left(\frac{197}{107}\right)^{\frac{1}{3}}=1.2256$

Hence, the ratio of the nuclear radii of the gold and silver isotopes is about 1.23.