# Suppose an attractive nuclear force acts between two protons which may be written as F = CE–kx/r2.(a) Write down the dimensional formulae and appropriate SI units of C and κ.(b) Suppose that κ = 1 fermi–1 and that the repulsive electric force between the protons is just balanced by the attractive nuclear force when the separation is 5 fermi. Find the value of C.

Given:

The attractive nuclear force between two protons is,

(a)The power of e must be dimensionless.

Thus,

Hence, SI unit of k is m.

Now,

Let us replace the formula with SI units

Hence, SI unit of C is Nm2

(b)

Given,

Separation between the protons, r = 5fermi = 5 × 10-15 m.

We know that the charge on a proton is q = 1.6 × 10-19C.

Now,

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Formula used:

By Coulomb’s law, the electric force is given by:

Where ϵ0 is the permittivity of free space

k is the electrostatic constant

q1 and q2 are the magnitude of charges

r is the distance of separation between the charges

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The electric force between the two protons is given by:

Also, the nuclear force between the protons is given by:

These two forces balance each other.

Fe=Fn

kq2=Ce-kr

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