(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.

Options

A. `7.68`
B. `-5.21`
C. `-0.48`
D. `9.34`

Answer

C

Explanation

Figure shows the quark model of neutron
Here, `r=10^(-15)` m
Potential energy of neutron is `U=1/(4piepsilon_0)[q_dq_d+q_uq_d+q_uq_d]`
`=(9xx10^9)/10^(-15)[("-e"/3)("-e"/3)+("2e"/3)("-e"/3)+("2e"/3)("-e"/3)]`
`=(9xx10^9)/(10^(-15))e^2 [1/9-4/9]=(9xx10^9)/(10^(-15)) (1.6xx10^(-19))^2(-1/3)`
`=-7.68xx10^(-14)J = -4.8xx10^5` eV
=-0.48 MeV