Question

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

Answer 1

Nuclear radius of the gold isotope $_{ 79} Au ^{197}$ = RAu
Nuclear radius of the silver isotope $_{47} Ag^{107}$ = RAg
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:
$\frac{R_{Au}}{R_{Ag}}$ = $(\frac{RAU}{RAG})^{\frac{1}{3}}$
= $(\frac{197}{107})^{\frac{1}{3}}$
= 1.2256
Hence, the ratio of the nuclear radii of the gold and silver isotopes is about 1.23