All nuclei consist of two types of particles- protaon and neutrons. Nuclear force is the strongest froce. Stability of nucleus is determined by the neutron - proton ratio or mass defect or binding energy per nucleus or packing fraction. Shape of nucleus is calculated by quadrupole moment. Spin of nucleus depends on even or odd mass number. Volume of nucleus depends on the mass number. Whole mass of the atom (nearly `99 %`) is centered at the nucleus. Magnetic moment of the nucleus is measured in terms of the nuclear magnetons.
Volume (V) of the nucleus is related to mass number (A) as

Options

A. `V prop A^(2)`
B. `V prop A^(1//3)`
C. `V prop A^(2//3)`
D. `V prop A`

Explanation

To find the relationship between the volume (V) of the nucleus and the mass number (A), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Radius of the Nucleus**:
The radius (r) of the nucleus is related to the mass number (A) by the formula:
\[ r = r_0 A^{1/3} \]
where \( r_0 \) is a constant.

2. **Calculating the Volume of the Nucleus**:
The volume (V) of a spherical nucleus can be calculated using the formula for the volume of a sphere:
\[ V = \frac{4}{3} \pi r^3 \]

3. **Substituting the Radius into the Volume Formula**:
Now, substitute the expression for r from step 1 into the volume formula:
\[ V = \frac{4}{3} \pi (r_0 A^{1/3})^3 \]

4. **Simplifying the Volume Expression**:
Simplifying the above expression gives:
\[ V = \frac{4}{3} \pi r_0^3 A \]
This shows that the volume of the nucleus is directly proportional to the mass number (A).

5. **Final Relationship**:
Therefore, we can conclude that:
\[ V \propto A \]
This means that the volume of the nucleus increases linearly with the mass number.