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
$U=\frac{1}{4\pi {\epsilon }_{0}r}\left[q_d{q}_d+q_u{q}_d+q_u{q}_d\right]$
$=\frac{9\times 10^9}{10^{-15}}\left[\left(\frac{-e}{3}\right)\left(\frac{-e}{3}\right)+\left(\frac{2e}{3}\right)\left(\frac{-e}{3}\right)+\left(\frac{2e}{3}\right)\left(\frac{-e}{3}\right)\right]$
$=\frac{9\times 10^9}{10^{-15}}{e}^2\left[\frac{1}{9}-\frac{4}{9}\right]$
$=\frac{9\times 10^9}{10^{-15}}{\left(1.6\times 10^{-19}\right)}^2\left(-\frac{1}{3}\right)$
$=-7.68\times 10^{-14}J$
$=-4.8\times 10^{5}eV$
$=-0.48MeV$