Q. 153.8( 8 Votes )

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.

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 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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