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 formula for a nucleus's radius is typically \(r = r_0 \cdot A^{1/3}\), where A denotes the mass number and \(r_0\) is a constant. Consequently, the ratio of the nuclear radii of two elements, \(\frac{r_A}{r_B}\), can be stated as:

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

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

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

Thus, the ratio of the nuclear radii is: 2 : 1