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

The radius of a nucleus is generally given by the formula \(r = r_0 \cdot A^{1/3}\), where A is the mass number, and \(r_0\) is a constant. Thus, the nuclear radius ratio of two elements \(\frac{r_A}{r_B}\) can be expressed as follows:

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

For the given elements with mass numbers \(A_A = 216\) and \(A_B = 27\), the ratio is computed as:

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

Therefore, the ratio of the nuclear radii is: 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)