Question

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 \(\frac{r_A}{r_B}\) of the two elements is:

• A. 2 : 1
• B. 4 : 1
• C. 6 : 1
• D. 8 : 1

Answer 1

The Correct Option is A

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

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

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

Answer 2

The nuclear radius (R) is related to mass number (A) by:

\[ R = R_0 A^{1/3} \]

where \( R_0 \) is a constant (~1.2 fm)

Ratio of radii:

\[ \frac{R_A}{R_B} = \left(\frac{A_A}{A_B}\right)^{1/3} = \left(\frac{216}{27}\right)^{1/3} \]

\[ \frac{R_A}{R_B} = 8^{1/3} = 2 \]

Answer: The ratio is \(\boxed{2 : 1}\) (Option 1)