Question

Calculate approximately the ratio of the nuclear radii of the gold isotope \[_{79}^{197}Au\] and the silver isotope \[_{47}^{107}Ag\].

Options

• 1.23

• 1.13

• 1.25

• 1.33

Answer 1

1.23

Explanation:

Given that,

Nuclear radius of the gold isotope ₇₉Au¹⁹⁷ = R_Au   

Nuclear radius of the silver isotope ₄₇Ag¹⁰⁷ = R_Ag 

Mass number of gold, A_Au = 197

Mass number of silver, A_Ag = 107

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

\[\frac{R_{\mathrm{Au}}}{R_{\mathrm{Ag}}}=\left(\frac{R_{\mathrm{Au}}}{R_{\mathrm{Ag}}}\right)^{\frac{1}{3}}=\left(\frac{197}{107}\right)^{\frac{1}{3}}=1.2256\]

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