(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.

Explanation

This system is made up of thre charges. The potential energy of the system is equal to the algebraic sum of PE of each pair. So,
`U=(1)/(4piepsi_(0)){(q_(d)q_(d))/(r)-(q_(u)d_(d))/(r)-(q_(u)q_(d))/(r)}`
`=(9xx10^(9))/(10^(-15))(1.6xx10^(-19))^(2)[{(1//3)^(2)-(2//3)(1//3)-(2//3)(1//3)}]`
`=2.304xx0^(-13){(1)/(9)-(4)/(9)}=-7.68xx10^(-14)J`
`=4.8xx10^(5)eV=0.48meV=5.11xx10^(-4)(m_(n)c^(2))`