Question

Obtain approximately the ratio of the nuclear radii of the gold isotope `""_97^197 "Au"` and the silver isotope `""_47^197"Ag"`.

Answer 1

Nuclear radius of the gold isotope `""_79"Au"^197` = R_Au

Nuclear radius of the silver isotope `""_47"Ag"^107` = 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 as:

`"R"_"Au"/"R"_"Ag" = ("R"_"Au"/"R"_"Ag")^(1/3)`

`= (197/107)^(1/3) = 1.2256`

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