Question

The ratio of the radii of the nucleus of two element X and Y having the mass numbers 232 and 29 is:

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

Hint:

The radius of a nucleus is proportional to the cube root of its mass number. For quick calculations, remember this relationship when comparing the radii of different nuclei.

Answer 1

The Correct Option is D

The radius \( r \) of a nucleus is given by the formula: \[ r = r_0 A^{1/3} \] where \( A \) is the mass number and \( r_0 \) is a constant. Now, the ratio of the radii of the two nuclei \( X \) and \( Y \) is: \[ \frac{r_X}{r_Y} = \frac{r_0 A_X^{1/3}}{r_0 A_Y^{1/3}} = \left( \frac{A_X}{A_Y} \right)^{1/3} \] Given that the mass numbers are \( A_X = 232 \) and \( A_Y = 29 \), we have: \[ \frac{r_X}{r_Y} = \left( \frac{232}{29} \right)^{1/3} \] \[ \frac{r_X}{r_Y} = \left( 8 \right)^{1/3} = 2 \] Thus, the ratio of the radii is \( 2 : 1 \).