As the mass number `A` increases, which of the following quantities related to a nucleus do not change?

Options

A. mass
B. volume
C. density
D. binding energy

Answer

To solve the question, "As the mass number `A` increases, which of the following quantities related to a nucleus do not change?", we will analyze the relationships between mass number `A` and various nuclear properties.

### Step-by-Step Solution:

1. **Understanding Mass Number (A)**:
- The mass number `A` is defined as the total number of protons and neutrons in a nucleus. As `A` increases, it indicates that either protons or neutrons (or both) are being added to the nucleus.

2. **Radius of the Nucleus**:
- The radius `r` of the nucleus is given by the formula:
\[ r = r_0 A^{1/3} \]
where \( r_0 \) is a constant (approximately 1.2 fm). As `A` increases, the radius `r` also increases. Therefore, the radius does change with increasing `A`.

3. **Volume of the Nucleus**:
- The volume `V` of the nucleus can be calculated using the formula:
\[ V = \frac{4}{3} \pi r^3 \]
Substituting the expression for `r`, we get:
\[ V = \frac{4}{3} \pi (r_0 A^{1/3})^3 = \frac{4}{3} \pi r_0^3 A \]
This shows that the volume is directly proportional to `A`, hence it also changes as `A` increases.

4. **Mass of the Nucleus**:
- The mass of the nucleus is given by:
\[ M = A \cdot m_n \]
where \( m_n \) is the mass of a nucleon (proton or neutron). As `A` increases, the mass `M` also increases. Thus, the mass changes with increasing `A`.

5. **Binding Energy**:
- The binding energy of a nucleus is related to the mass number and also changes as `A` increases. It is influenced by the strong nuclear force and the arrangement of nucleons. Therefore, binding energy also changes with increasing `A`.

6. **Density of the Nucleus**:
- Density `D` is defined as mass per unit volume:
\[ D = \frac{M}{V} \]
Substituting the expressions for `M` and `V`, we have:
\[ D = \frac{A \cdot m_n}{\frac{4}{3} \pi r_0^3 A} = \frac{3 m_n}{4 \pi r_0^3} \]
This shows that the density is independent of `A` since `A` cancels out. Therefore, as `A` increases, the density remains constant.

### Conclusion:
From the analysis, the quantity that does not change as the mass number `A` increases is the **density of the nucleus**.

### Final Answer:
The quantity that does not change as the mass number `A` increases is **density**.