(a) Show that all combinations of three quarks produce integral charges. Thus, baryons must have integral charge.

(b) Show that all combinations of a quark and an antiquark produce only integral charges. Thus, mesons must have integral charge.

A baryon is a type of composite subatomic particle in particle physics category which contains an odd number of valence quarks.

A quark is defined as the basic ingredient of matter and a sort of elementary particle.

Antiquarks are defined as the antiparticles that correspond to each flavour of quark.

(a)

Since baryons are formed by combinations of \({\rm{3}}\) quarks, and since there are only two charges for the quarks: \(\frac{{{\rm{ - 1}}}}{{\rm{3}}}\) and \(\frac{{\rm{2}}}{{\rm{3}}}\), then there would be \(4\) combinations of those quarks such that –

First combination;

\(\frac{{ - 1}}{3} + \frac{{ - 1}}{3} + \frac{{ - 1}}{3} = - 1\)

Second combination;

\(\frac{{ - 1}}{3} + \frac{{ - 1}}{3} + \frac{2}{3} = 0\)

Third combination;

\(\frac{2}{3} + \frac{2}{3} + \frac{2}{3} = 2\)

Fourth combination;

\(\frac{{ - 1}}{3} + \frac{2}{3} + \frac{2}{3} = 1\)

As here all the combination of three quarks produce integral charges. This leads to the fact that baryons must have integral charge.

Therefore, baryons have integral charge.

(b)

Since mesons are formed by combinations of one quark and one antiquark, and since there are only two charges for the quarks: \(\frac{{{\rm{ - 1}}}}{{\rm{3}}}\) and \(\frac{{\rm{2}}}{{\rm{3}}}\), and only two charges for the antiquarks: \(\frac{{\rm{1}}}{{\rm{3}}}\) and \(\frac{{{\rm{ - 2}}}}{{\rm{3}}}\) then there would be \(4\) forms of those mesons given by –

First combination;

\(\frac{2}{3} + \frac{1}{3} = 1\)

Second combination;

\(\frac{2}{3} - \frac{1}{3} = 0\)

Third combination;

\(\frac{{ - 1}}{3} + \frac{1}{3} = 0\)

Fourth combination;

\(\frac{{ - 1}}{3} - \frac{2}{3} = - 1\)

As here all the combination of quarks produce integral charges. This leads to the fact that mesons must have integral charge.

Therefore, mesons have integral charge.