Question 45: Atoms & Nuclei

Question

The ratio of the radii of the nucleus of two element $\mathrm{X}$ and $\mathrm{Y}$ having the mass numbers 232 and 29 is:

Accepted Answer

The radius of a nucleus is related to the mass number (A) by the formula:
$R = R_0 \cdot A^{1/3}$
where:
$R_0$ is a constant (approximately $1.2 	imes 10^{-15}$ meters), and
$A$ is the mass number.
Let's denote the radii of the nuclei of elements $\mathrm{X}$ and $\mathrm{Y}$ by $R(\mathrm{X})$ and $R(\mathrm{Y})$ respectively. Given the mass numbers:
For element $\mathrm{X}$: $A(\mathrm{X}) = 232$
For element $\mathrm{Y}$: $A(\mathrm{Y}) = 29$
The radii are then:
$R(\mathrm{X}) = R_0 \cdot (232)^{1/3}$
$R(\mathrm{Y}) = R_0 \cdot (29)^{1/3}$
We are asked to find the ratio of these radii:
$\frac{R(\mathrm{X})}{R(\mathrm{Y})} = \frac{R_0 \cdot (232)^{1/3}}{R_0 \cdot (29)^{1/3}} = \left(\frac{232}{29}ight)^{1/3}$
Calculating the cube root of the ratio:
$\frac{232}{29} \approx 8$
$8^{1/3} = 2$
Hence, the ratio of the radii of the nuclei of elements $\mathrm{X}$ and $\mathrm{Y}$ is:
$2:1$
The correct option is
Option D: 2 : 1
.

Answer

4 : 1

Answer

1 : 4

Answer

1 : 2

Answer

2 : 1

Atoms & Nuclei

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

Choose the correct answer: