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: