If A is mass number of a nucleus of Radius R, then

Options

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

Answer

To solve the problem, we need to understand the relationship between the mass number (A) of a nucleus and its radius (R). The relationship is given by the formula:

\[ R = R_0 \cdot A^{1/3} \]

where \( R_0 \) is a constant.

### Step-by-Step Solution:

1. **Understand the Formula**: The formula states that the radius \( R \) of a nucleus is proportional to the cube root of its mass number \( A \). Here, \( R_0 \) is a constant that has a specific value.

2. **Substitute the Value of \( R_0 \)**: The value of \( R_0 \) is given as \( 1.25 \times 10^{-15} \) meters. This value is used to calculate the radius for a given mass number.

3. **Cube the Radius Formula**: To find a relationship between \( A \) and \( R \), we can cube both sides of the equation:
\[ R^3 = (R_0 \cdot A^{1/3})^3 \]
This simplifies to:
\[ R^3 = R_0^3 \cdot A \]
Here, \( R_0^3 \) is a constant.

4. **Establish the Proportional Relationship**: From the equation \( R^3 = R_0^3 \cdot A \), we can see that \( A \) is directly proportional to \( R^3 \):
\[ A \propto R^3 \]

5. **Conclusion**: Therefore, we conclude that the mass number \( A \) of a nucleus is directly proportional to the cube of its radius \( R \). This relationship confirms that if the radius increases, the mass number also increases proportionally to the cube of the radius.

### Final Answer:
The mass number \( A \) is directly proportional to the cube of the radius \( R \) of the nucleus.