`F_(pp),F_("nn")and F_(np) ` are the nuclear forces between proton - proton , neutron - neutron and neutron - proton respectively . Then relation between them is

Options

A. (a)`F_(pp)=F_("nn")ne F_(np) `
B. (b)`F_(pp)neF_("nn")= F_(np) `
C. (c)`F_(pp)=F_("nn")= F_(np) `
D. (d)`F_(pp)neF_("nn")ne F_(np) `

Answer

To solve the problem regarding the relationship between the nuclear forces \( F_{pp} \) (proton-proton), \( F_{nn} \) (neutron-neutron), and \( F_{np} \) (neutron-proton), we can follow these steps:

### Step 1: Understanding Nuclear Forces
Nuclear forces are the interactions that hold the nucleus of an atom together. They are strong forces that act between nucleons (protons and neutrons). One key characteristic of these forces is that they do not depend on the electric charge of the particles involved.

### Step 2: Analyzing the Forces
1. **Proton-Proton Force (\( F_{pp} \))**: This is the force between two protons.
2. **Neutron-Neutron Force (\( F_{nn} \))**: This is the force between two neutrons.
3. **Neutron-Proton Force (\( F_{np} \))**: This is the force between a neutron and a proton.

### Step 3: Establishing Relationships
Since nuclear forces are strong and do not depend on the charge of the particles, we can state that:
- The force between two protons \( F_{pp} \) is equal to the force between two neutrons \( F_{nn} \).
- The force between a neutron and a proton \( F_{np} \) is also comparable to the other two forces.

Thus, we can write:
\[ F_{pp} = F_{nn} = F_{np} \]

### Step 4: Conclusion
From the above analysis, we conclude that all three forces are equal. Therefore, the relationship can be summarized as:
\[ F_{pp} = F_{nn} = F_{np} \]

### Final Answer
The correct relation between the nuclear forces is:
\[ F_{pp} = F_{nn} = F_{np} \]