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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