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 order of $10^{- 15}$m. The electrostatic potential energy of neutron in Me V is

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

Answer 1

Answer: (C)

-0.48

Answer 2

: Figure shows the quark model of neutron Here, $r = 10^{- 15}m$ Potential energy of neutron is.

$U = \frac{1}{4\pi\varepsilon_{0}r}\lbrack q_{d}q_{d} + q_{u}q_{d} + q_{u}q$

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

$= \frac{9 \times 10^{9}}{10^{- 15}}e^{2}\left\lbrack \frac{1}{9} - \frac{4}{9} \right\rbrack = \frac{9 \times 10^{9}}{10^{- 15}}(1.6 \times 10^{- 19})^{2}\left( - \frac{1}{3} \right)$

$= - 7.68 \times 10^{- 14}J = - 4.8 \times 10^{5}eV$

$= - 0.48MeV$