(a) In a quark model of elementary particles, a neutron is made of one up quarks [charge (2/3) e] and two down quarks [charges – (1/3) e]. Assume that they have a triangle configuration with side length of the order of 10–15 m. Calculate electrostatic potential energy of neutron and compare it with its mass 939 MeV.
(b) Repeat above exercise for a proton which is made of two up and one down quark.
(a)
Given
Number of up quarks for neutron = 1
Number of down quarks for neutron = 2
Charge on an up quark = 
e
Charge on a down quark = 
e
Distance between each quark = 10–15 m
The quarks are arranged on the vertices of a an equilateral triangle with side 
m. The potential energy between two charges is given by the equation
The potential energy of the given triangular system with three charges (quarks are considered charges here) can be obtained by the algebraic sum of the potential energy of each pair.
Where 
and 
, e=
By comparing this energy with the neutrons mass (939 MeV) we find that this potential energy is equivalent to
neutron masses
(b)
Given
Number of up quarks for neutron = 2
Number of down quarks for neutron = 1
Charge on an up quark = 
e
Charge on a down quark = 
e
Distance between each quark = 10–15 m
For a proton with this arrangement of quarks the potential energy is given by
