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,
_________________________________________________
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
__________________________________________________
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
