Question

(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.

Answer 1

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))`