Two nucleons are at a separation of `1 xx 10^-15 m`. The net force between them is `F_1`, if both are neutrons, `F_2` if both are protons and `F_3` if one is a proton and other is a neutron. In such a case.

Options

A. `F_(2)gtF_(1)gtF_(3)`
B. `F_(1)=F_(2)=F_(3)`
C. `F_(1)=F_(2)gtF_(3)`
D. `F_(1)=F_(3)gtF_(2)`

Answer

To solve the problem, we need to analyze the forces acting between different combinations of nucleons (neutrons and protons) at a separation of \(1 \times 10^{-15} \, \text{m}\).

### Step-by-Step Solution:

1. **Understanding Nuclear Forces**:
- The forces acting between nucleons (neutrons and protons) at very short distances (on the order of \(1 \times 10^{-15} \, \text{m}\)) are called nuclear forces. These forces are responsible for holding the nucleons together in the nucleus of an atom.

2. **Identifying the Combinations**:
- We have three combinations to consider:
- \(F_1\): Force between two neutrons.
- \(F_2\): Force between two protons.
- \(F_3\): Force between one proton and one neutron.

3. **Properties of Nuclear Forces**:
- One of the key properties of nuclear forces is that they are **charge-independent**. This means that the strength of the nuclear force does not depend on whether the nucleons are protons or neutrons.

4. **Applying Charge Independence**:
- Since the nuclear force is independent of the type of nucleons involved, we can conclude that:
- The force between two neutrons (\(F_1\)) is equal to the force between two protons (\(F_2\)), and it is also equal to the force between one proton and one neutron (\(F_3\)).
- Mathematically, we can express this as:
\[ F_1 = F_2 = F_3 \]

5. **Conclusion**:
- Therefore, the net forces between the nucleons can be summarized as:
\[ F_1 = F_2 = F_3 \]
- The correct answer is that all three forces are equal.

### Final Answer:
- \(F_1 = F_2 = F_3\)