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  4. The nuclear radius of a certain nucleus is 7.2 fm and it has charge of 1.28× 10-17C . The number of neutrons inside the nucleus is

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Q. The nuclear radius of a certain nucleus is $ 7.2 \,fm $ and it has charge of $ 1.28\times {{10}^{-17}}C $ . The number of neutrons inside the nucleus is

KEAMKEAM 2008

Solution:

$ R={{R}_{0}}{{A}^{1/3}} $
Here, $ R=7.2\times {{10}^{-15}}m,{{R}_{0}}=1.2\times {{10}^{-15}}m $
$ \therefore $ $ A={{\left( \frac{R}{{{R}_{0}}} \right)}^{3}}=\left( \frac{7.2\times {{10}^{-15}}}{1.2\times {{10}^{-15}}} \right)={{(6)}^{3}}=216 $
Also, atomic number $ Z=\frac{q}{e}=\frac{1.28\times {{10}^{-17}}}{1.6\times {{10}^{-19}}}=80 $ Therefore, number of neutrons $ N=A-Z=216-80=136 $