`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. `F_(pp)=F_("nn")ne F_(np) `
B. `F_(pp)neF_("nn")= F_(np) `
C. `F_(pp)=F_("nn")= F_(np) `
D. `F_(pp)neF_("nn")ne F_(np) `

Answer

To solve the problem regarding the relationship between the nuclear forces \( F_{pp} \), \( F_{nn} \), and \( F_{np} \), we can analyze the nature of these forces step by step.

### Step 1: Understand the Definitions
- \( F_{pp} \): This is the nuclear force between two protons.
- \( F_{nn} \): This is the nuclear force between two neutrons.
- \( F_{np} \): This is the nuclear force between a neutron and a proton.

### Step 2: Recognize the Characteristics of Nuclear Forces
Nuclear forces are known to be:
- Very strong compared to other forces like the electromagnetic force.
- Short-ranged, meaning they only act over very small distances (on the order of femtometers).

### Step 3: Analyze the Dependence of Nuclear Forces
Nuclear forces do not depend on the specific type of nucleons (protons or neutrons) involved in the interaction. Instead, they depend primarily on the distance between the nucleons. The strength of the force is similar for different combinations of nucleons when they are within the effective range of the nuclear force.

### Step 4: Establish the Relationship
Given the above characteristics, we can conclude that:
- The nuclear force between two protons (\( F_{pp} \)) is comparable to the nuclear force between two neutrons (\( F_{nn} \)), and both are comparable to the nuclear force between a neutron and a proton (\( F_{np} \)).
- Therefore, we can express the relationship as:
\[ F_{pp} \approx F_{nn} \approx F_{np} \]

### Conclusion
The relationship between the nuclear forces can be summarized as:
\[ F_{pp} = F_{nn} = F_{np} \]