Q. 153.8( 8 Votes )

# Suppose an attractive nuclear force acts between two protons which may be written as F = CE^{–kx}/r^{2}.

(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.

Answer :

__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 Nm^{2}

(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^{-19}C.

Now,

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**Formula used:**

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

Where ϵ_{0} is the permittivity of free space

k is the electrostatic constant

q_{1} and q_{2} 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.

F_{e}=F_{n}

kq^{2}=Ce^{-kr}

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