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`

Answer

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

### Step 1: Understand the relationship between the radius of the nucleus and the mass number
The radius (R) of the nucleus is given by the formula:
\[ R = R_0 \cdot A^{1/3} \]
where \( R_0 \) is a constant.

### Step 2: Relate the volume of the nucleus to its radius
The volume (V) of a sphere (which we can approximate the nucleus to be) is given by the formula:
\[ V = \frac{4}{3} \pi R^3 \]

### Step 3: Substitute the expression for the radius into the volume formula
Substituting the expression for R from Step 1 into the volume formula:
\[ V = \frac{4}{3} \pi (R_0 \cdot A^{1/3})^3 \]

### Step 4: Simplify the volume expression
Calculating \( (R_0 \cdot A^{1/3})^3 \):
\[ V = \frac{4}{3} \pi R_0^3 \cdot A \]
This shows that the volume of the nucleus is directly proportional to the mass number (A).

### Step 5: Conclude the relationship
Thus, we can conclude that:
\[ V \propto A \]
This means that the volume of the nucleus is directly proportional to its mass number.

### Final Answer
The volume (V) of the nucleus is related to the mass number (A) as:
\[ V \propto A \]

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