Nuclei - Result Question 2
2. If the nuclear radius of ${ }^{27} Al$ is 3.6 Fermi, the approximate nuclear radius of ${ }^{64} Cu$ in Fermi is :
(a) 2.4
(b) 1.2
(c) 4.8
(d) 3.6
[2012]
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Answer:
Correct Answer: 2. (c)
Solution:
- (c) The radius of the nuclears is directly proportional to cube root of atomic number i.e. $R \propto A^{1 / 3}$
$R=R_0 A^{1 / 3}$, where $R_0$ is a constant of proportionality
$\frac{R_2}{R_1}=(\frac{A_2}{A_1})^{1 / 3} \Rightarrow(\frac{64}{27})^{1 / 3}=\frac{4}{3}$
where $R_1=$ the radius of ${ }^{27} Al$, and $A_1=$ Atomic mass number of $A 1$
$R_2=$ the radius of ${ }^{64} Cu$ and $A_2=$ Atomic mass number of $C 4$
$ R_2=3.6 \times \frac{4}{3}=4.8 m $
