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Physics Question on Atoms and Nuclei

As per Nuclear Physics, there is a close relationship between mass num ber and radius of the nucleus. If the mass number of A is 216 and the mass number of B is 27, then the ratio of nuclear radius rArB\frac{r_A}{r_B} of the two elements is:

A

2 : 1

B

4 : 1

C

6 : 1

D

8 : 1

Answer

2 : 1

Explanation

Solution

 The nuclear radius r is related to the mass number A as:\text{ The nuclear radius } r \text{ is related to the mass number } A \text{ as:}
rA1/3r \propto A^{1/3}
Thus, the ratio of the nuclear radii of A and B is given by:\text{Thus, the ratio of the nuclear radii of A and B is given by:}

rArB=(AAAB)1/3=(21627)1/3=(8)1/3=2\frac{r_A}{r_B} = \left( \frac{A_A}{A_B} \right)^{1/3} = \left( \frac{216}{27} \right)^{1/3} = (8)^{1/3} = 2

Thus, the correct answer is (1)2:1.\text{Thus, the correct answer is } (1) \, 2 : 1.