Question

In a quark model of elemetary particles, a neutron is made of one up quark of charge $\frac{2}{3}e$ and two down quark of charges $(-\frac{1}{3}e)$. If they have a triangle configuration with side length of the order of ${10}^{-15}m$. The electrostatic potential energy of neutron in $MeV$ is

• A. $7.68$
• B. $-5.21$
• C. $-.048$
• D. $9.34$

Answer 1

Answer: (C)

$-.048$

Fig shows the quark model of a neutral, where $r={10}^{-15}m$.

Potential energy of neutron

$V=\frac{1}{4\pi {ϵ}_{0}r}[q_e{q}_d+q_u{q}_d+q_u{q}_d]$

$=\frac{9\times {10}^9}{{10}^{-15}}[(-\frac{e}{3})(-\frac{e}{3})+\left(\frac{2e}{3}\right)(-\frac{e}{3})+\left(\frac{2e}{3}\right)(-\frac{e}{3})]$

$V=\frac{9\times {10}^9}{{10}^{-15}}(\frac{1}{9}-\frac{4}{9})(1.6\times {10}^{-19}{)}^2=-7.68\times {10}^{-14}J$

$V=\frac{-7.68\times {10}^{-14}}{1.6\times {10}^{-19}}eV=-4.8\times {10}^{5}eV=-0.48MeV$