Obtain approximately the ratio of the nuclear radii of the gold isotope $^{197}_{79} Au$ and the silver isotope $^{107}_{47} Ag$ .
Obtain approximately the ratio of the nuclear radii of the gold isotope $^{197}_{79} Au$ and the silver isotope $^{107}_{47} Ag$ .
Nuclear radius of the gold isotope $_{\tau g} A u^{197}=R_{A u}$
Nuclear radius of the silver isotope $_{47} A g^{107}=R_{4 g}$
Mass number of gold, $A_{A u}=197$
Mass number of silver, $A_{A g}=107$
The ratio of the radii of the two nuclei is related with their mass numbers as
$\left( R _{ A w } / R _{ A g }\right)=\left( A _{ A u } / A _{ A g }\right)^{1 / 3}=1.2256$
Hence, the ratio of the nuclear radii of the gold and silver isotopes is about $1.23$
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- [AIEEE 2004]