Ncert Exercises & Solutions

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

Hint: Nuclear radius is given by, \(R=R_oA^{1/3}\).
Step 1: Find the mass numbers of \({ }_{79}^{197} \mathrm{Au}\) and \({ }_{47}^{107} \mathrm{Ag}\).
Nuclear radius of the gold isotope

{}_{79}^{197}{Au} = R_{Au}

Nuclear radius of the silver isotope

{}_{47}^{107}{Ag} = R_{Ag}

Mass number of gold, \(\mathrm{A}_{\mathrm{Au}}=197\)
Mass number of silver, \(\mathrm{A}_{\mathrm{Ag}}=107\)
Step 2: Find the ratio of nuclear radii of \({ }_{79}^{197} \mathrm{Au}\) and \({ }_{47}^{107} \mathrm{Ag}\).

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

\frac{R_{Au}}{R_{Ag}} = {(\frac{A_{Au}}{A_{Ag}})}^{\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

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