Question

In a quark model of elementary particles, a neutron is made of one up quark of charge $\frac{2}{3}e$ and two down quark of charges $\left(-\frac{1}{3}e\right)$. 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. $-0.48$
• D. $9.34$

Answer 1

Answer: (C)

Figure shows the quark model of neutron

Here, $r=10^{-15}\,m$
Potential energy of neutron is
$U=\frac{1}{4\pi\varepsilon_{0}r} \left[q_{d} q_{d}+q_{u}q_{d}+q_{u}q_{d}\right]$
$=\frac{9\times10^{9}}{10^{-15}} \left[\left(\frac{-e}{3}\right)\left(\frac{-e}{3}\right)+\left(\frac{2e}{3}\right)\left(\frac{-e}{3}\right)+\left(\frac{2e}{3}\right)\left(\frac{-e}{3}\right)\right]$
$=\frac{9\times10^{9}}{10^{-15}}e^{2}\left[\frac{1}{9}-\frac{4}{9}\right]$
$=\frac{9\times10^{9}}{10^{-15}}\left(1.6\times10^{-19}\right)^{2} \left(-\frac{1}{3}\right)$
$=-7.68\times10^{-14} \,J $
$=-4.8\times10^{5}\,eV$
$=-0.48 \,MeV$