Which of the following is not an assumption involved in the expresssion: `r=(1.2xx10^(-15)m)A^(1//3)`?

Options

A. Nuclei are incompressible.
B. The nucleus is spherical in shape.
C. All nucleons have roughtly the same mass.
D. Nuclear densities are proportional to the mass numbers.

Answer

To solve the question, we need to identify which of the given options is not an assumption involved in the expression for the radius of the nucleus given by \( r = (1.2 \times 10^{-15} \, \text{m}) A^{1/3} \).

### Step-by-Step Solution:

1. **Understanding the Formula**:
The formula \( r = (1.2 \times 10^{-15} \, \text{m}) A^{1/3} \) is used to calculate the radius of a nucleus, where \( A \) is the mass number (the total number of protons and neutrons in the nucleus).

2. **Identifying Assumptions**:
We need to analyze the assumptions that are typically made when deriving this formula:
- **Assumption 1**: Nuclei are incompressible. This means that the volume does not change under pressure, which is a valid assumption for nuclear physics.
- **Assumption 2**: Nuclei are spherical in shape. This assumption is also valid because the formula uses the volume of a sphere to derive the radius.
- **Assumption 3**: All nucleons (protons and neutrons) have roughly the same mass. This is true since we consider the mass number \( A \) as a sum of nearly equal masses of nucleons.
- **Assumption 4**: Nuclear densities are proportional to mass numbers. This assumption is incorrect. The correct assumption is that nuclear densities are independent of mass numbers; they remain approximately constant across different nuclei.

3. **Conclusion**:
Since we are looking for the assumption that is not involved in the expression, we find that the statement regarding nuclear densities being proportional to mass numbers is incorrect. Therefore, this is the option that does not represent an assumption used in the derivation of the formula.

### Final Answer:
The option that is **not an assumption** involved in the expression is: **Nuclear densities are proportional to mass numbers**.

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