Question

It is now established that protons and neutrons (which constitute nuclei of ordinary matter) are themselves built out of more elementary units called quarks. A proton and a neutron consist of three quarks each. Two types of quarks, the so called ‘up’ quark (denoted by u) of charge $+\left(\frac{2}{3}\right)e$, and the ‘down’ quark (denoted by d) of charge $1\left(\frac{1}{3}\right)e$, together with electrons build up ordinary matter. (Quarks of other types have also been found which give rise to different unusual varieties of matter.) Suggest a possible quark composition of a proton and neutron.

Answer 1

A proton has three quarks. Let there be $n$ ‘up’ quarks in a proton, each having a charge of $+\left(\frac{2}{3}\right)e,$
Charge due to 𝑛 ‘up’ quarks $+\left(\frac{2}{3}e\right)\times n$
Number of ‘down’ quarks in a proton $=3-n$
Each down quark has a charge of $-\left(\frac{1}{3}\right)e$
Charge due to $(3-n)$ 'down' quarks $=(-\frac{1}{3}e)\times (3-n)$
Total charge on a proton $=+e$
$e=\left(\frac{2}{3}e\right)\times n+(-\frac{1}{3}e)\times (3-n)$
$e=\frac{2}{3}ne-e+\frac{1}{2}ne$
$\Rightarrow n=2$
Therefore, Number of ‘up’ quarks in a proton $n=2$
Number of ‘down’ quarks in a proton $=3-n=3-2=1$
A neuron also has three quarks. Let there be $n$ ‘up’ quarks in a neutron
Charge due to $n$ ‘up’ quarks $=\left(\frac{2}{3}e\right)\times n$
Number of down quarks in a proton $=3-n$
Each down quark has a charge of $=\left(\frac{1}{3}\right)e$
Charge due to $3-n$ ‘down’ quarks $=(-\frac{1}{3}e)\times (3-n)$
Total charge on a neutron =$0$
$0=\left(\frac{2}{3}e\right)\times n+(-\frac{1}{3}e)\times (3-n)$
$0-\frac{2}{3}ne-e+\frac{1}{3}ne\Rightarrow n=1$
Number of ‘up’ quarks in a neutron, $n=1$
Number of ‘down’ quarks in a neutron $=3-n=2$