Question

The mass number of two nuclei P and Q are 27 and 125 respectively. The ratio of their radii \( R_P : R_Q \) is given by:

• A. 9 : 25
• B. 3 : 5
• C. 27 : 25
• D. 5 : 3

Hint:

The relationship between the radii of atomic nuclei and their mass numbers is directly proportional to \( A^{1/3} \), where \( A \) is the mass number of the nucleus.

Answer 1

The Correct Option is B

The radii of atomic nuclei are related to their mass number by the following formula: \[ R \propto A^{1/3} \] Where \( A \) is the mass number of the nucleus. Given that the mass numbers of nuclei P and Q are 27 and 125 respectively, the ratio of their radii \( R_P : R_Q \) is: \[ \frac{R_P}{R_Q} = \left(\frac{A_P}{A_Q}\right)^{1/3} = \left(\frac{27}{125}\right)^{1/3} \] Now, simplifying: \[ \frac{R_P}{R_Q} = \left(\frac{27}{125}\right)^{1/3} = \left(\frac{3^3}{5^3}\right)^{1/3} = \frac{3}{5} \] Thus, the ratio of the radii is \( 3 : 5 \).