Obtain approximately the ratio of the ...

NCERT Class XII Chapter
Nuclei
Questions With Solutions

Question : 11 of 31

Marks: +1, -0

Obtain approximately the ratio of the nuclear radii of the gold isotope

{}^{197}_{79}\mathrm{Au}

and the silver isotope

{}^{\, {\underset{47}{107}\mathrm{Ag}}}

Solution:

We know the radius of nucleus depend upon mass number ‘A’

As R =

R_0 A^{\frac{1}{3}}

, where

R_0

= 1.1 ×

10^{-15}

∴

\frac{R(\,{}^{197}\mathrm{Au})}{R(\,{}^{107}\mathrm{Ag})}

\left(\frac{197}{107}\right)^{\frac{1}{3}}

= 1.23

Since the nuclear mass density is independent of the size of the nucleus,

\frac{\rho_{\nu}(\mathrm{Au})}{\rho_{\nu}(\mathrm{Ag})}

= 1

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