Suppose F_ pp , F_ pn , and F_ nn represent the magnitudes of the...

The strong nuclear force is a fundamental force that acts between nucleons (protons and neutrons).

One of the key properties of the strong nuclear force is that it is charge-independent. This means that the nuclear force between any two nucleons does not depend on their electric charges.

Therefore, for a given separation distance (such as $1 \text{ fm}$), the magnitude of the nuclear force between two protons ($F_{pp}$), a proton and a neutron ($F_{pn}$), and two neutrons ($F_{nn}$) is exactly the same.

$F_{pp} = F_{pn} = F_{nn}$