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Q. The radius of a spherical nucleus as measured by electron scattering is $3.6 \,fm$. What is the likely mass number of the nucleus?

UP CPMTUP CPMT 2015Nuclei

Solution:

Nuclear radius $R=R_{0}\left(A\right)^{1/ 3}$
where $A$ is the mass number of a nucleus
Given : $R = 3.6\, fm$
$\therefore \, 3.6\,fm =\left(1.2\,fm\right)\left(A^{1 /3}\right) \left[\because\, R_{0}=1.2\,fm\right]$
or $A=\left(3\right)^{3}=27$