Let `F_pp, F_pn and F_nn` denote the magnitudes of the nuclear force by a proton on a proton, by a proton on a neutron and by a neutron on a neutron respectively. When the separation is `1 fm`,

Options

A. `F_(pp) gt F_(pn) = F_(n n)`
B. `F_(pp) =F_(pn) =F_(n n)`
C. `F_(pp) gt F_(pn) gt F_(n n)`
D. `F_(pp) lt F_(pn) = F_(n n)`

Explanation

To solve the problem, we need to analyze the forces acting between protons and neutrons at a separation of 1 femtometer (fm). We denote the forces as follows:

- \( F_{pp} \): the force exerted by a proton on another proton.
- \( F_{pn} \): the force exerted by a proton on a neutron.
- \( F_{nn} \): the force exerted by a neutron on another neutron.

### Step-by-Step Solution:

1. **Understanding the Nature of the Particles**:
- Protons are positively charged particles, while neutrons are neutral. This difference in charge will affect the forces between them.

2. **Analyzing the Forces**:
- When two protons approach each other, they repel each other due to their like charges. Therefore, the force \( F_{pp} \) (force between two protons) will be a repulsive force.
- A proton and a neutron, however, will experience an attractive force due to the strong nuclear force, which is effective even at very short distances. Thus, \( F_{pn} \) (force from a proton on a neutron) will be attractive.
- Neutrons also interact with each other through the strong nuclear force, which is attractive as well. Therefore, \( F_{nn} \) (force between two neutrons) will also be attractive.

3. **Comparing the Magnitudes of Forces**:
- Since \( F_{pp} \) is a repulsive force, it is generally weaker than the attractive forces \( F_{pn} \) and \( F_{nn} \).
- The attractive force \( F_{pn} \) (proton on neutron) is stronger than the repulsive force \( F_{pp} \) (proton on proton) because the strong nuclear force is effective in binding nucleons (protons and neutrons) together.
- The force \( F_{nn} \) (neutron on neutron) is also attractive and is comparable to \( F_{pn} \).

4. **Establishing the Relationships**:
- From the above analysis, we can establish the following relationships:
\[ F_{pp} < F_{pn} = F_{nn} \]

### Final Conclusion:
Thus, the correct relationship between the forces is:
\[ F_{pp} < F_{pn} = F_{nn} \]