Answer
In order to double the nuclear radius number of nucleons has to be increased by a factor of $1.2599$
Work Step by Step
Nuclear radius is given by
$r=(1.2\times10^{-15}m)A^{\frac{1}{3}}$.........(1)
here $A$ is number of nucleon number of the nucleus.
I want Radius to be double
so new radius $r_{double}=2r$ ........(2)
and in double nucleus radius suppose number of nucleon is $A_{new}$
so
$r_{double}=(1.2\times10^{-15}m)A_{new}^{\frac{1}{3}}$.....(3)
from equation (1) and (3) putting the value in equation (2) will give us
$(1.2\times10^{-15}m)A_{new}^{\frac{1}{3}}=2\times(1.2\times10^{-15}m)A^{\frac{1}{3}}$
$A_{new}^{\frac{1}{3}}=2A^{\frac{1}{3}}$
$A_{new}=(2)^{\frac{1}{3}}A$
$A_{new}=1.2599A$
so in order to double the nuclear radius number of nucleons has to be increased by a factor of $1.2599$
