Answer
Unknown nucleus is isotope of hydrogen tritium $ ^{3}_{1}T$
(note:- no considerable change of nucleons observed)
Work Step by Step
$ ^{3}_{1}T$
Comparing with $ ^{A}_{Z}X$
we get
$A=3$
$Z=1$
number of neutrons $N=A-Z$
$N=3-1=2$
no of neutron in tritium is $N=2$
Suppose radius of tritium is $r_{T}$
so from equation number 31.2
$r_{T}=(1.2\times10^{-15}m)A_{T}^{\frac{1}{3}}$
for tritium $A_{T}=3$
$r_{T}=(1.2\times10^{-15}m)(3)^{\frac{1}{3}}$...................equation(1)
Suppose for for unknown nucleus $ ^{A}_{Z}X$ radius is $r_{X}$
if its nucleon number is $A$ radius will be
(again from equation number 31.2)
$r_{X}=(1.2\times10^{-15}m)A^{\frac{1}{3}}$..............equation(2)
given that
$\frac{r_{X}}{r_{T}}=1.10$
putting the values of $r_{T}$ and $r_{X}$ from equation (1) and (2) we will get
$\frac{(1.2\times10^{-15}m)A^{\frac{1}{3}}}{(1.2\times10^{-15}m)(3)^{\frac{1}{3}}}=1.10$
$A^{\frac{1}{3}}=1.10\times 3^{\frac{1}{3}}$
or $A=(1.10)^{\frac{1}{3}}\times 3=1.03228\times 3$
$A=3.0968\approx3$
now if the number of neutrons are same $N=2$
$Z=A-N$=$1$ so unknown nucleus is isotope of hydrogen tritium
$ ^{3}_{1}T$
