Verify the quantum numbers given for the proton and neutron in Table \[33.2\] by adding the quantum numbers for their quark constituents as given in Table \[33.4\].

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

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

Prove the quantum numbers for proton and neutron by using its quark compositions. Thus, the quantum numbers for proton and neutron from table\[{\rm{33}}{\rm{.2}}\]is –

Now, from table\[{\rm{33}}{\rm{.4}}\], the quark compositions for\[{\rm{p}}\]and\[{\rm{n}}\]is –

\[\begin{array}{l}p = \left[ {uud} \right]\\n = \left[ {udd} \right]\end{array}\]

So, now for proton it is obtained –

\[\begin{array}{c}B = \frac{1}{3} + \frac{1}{3} + \frac{1}{3} = 1\\S = 0 + 0 + 0 = 0\end{array}\]

Since, it is a baryon not a lepton. So, it is obtained –

\[{L_e} = {L_\mu } = {L_\tau } = 0\]

So, now for neutron it is obtained –

\[\begin{array}{c}B = \frac{1}{3} + \frac{1}{3} + \frac{1}{3} = 1\\S = 0 + 0 + 0 = 0\end{array}\]

Since, it is a baryon not a lepton. So, it is obtained –

\[{L_e} = {L_\mu } = {L_\tau } = 0\]

Therefore, from the quark compositions for\[{\rm{p}}\]and\[{\rm{n}}\], it can be proved that its quantum numbers are given in table \[{\rm{33}}{\rm{.2}}\].