It is now believed 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 + (2/3) e, and the ‘down’ quark (denoted by d) of charge (–1/3) 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.

A proton has three quarks. Let there be n up quarks in a proton, each having a charge of (+2/3) e.

Charge due to n up quarks =(2/3 x e)n

Number of down quarks in a proton = 3 – n

Each down quark has a charge of = -1/3 x e

Charge due to (3 – n) down quarks =  (-1/3 x e) (3 — n)

Total charge on a proton = + e

_{Therefore e =} (2/3 x e) n ₊ (-1/3 x e) (3 — n)

=> e = 2ne/3  – e + ne/3

=> 2 e = ne => n = 2

Number of up quarks in a proton, n = 2

Number of down quarks in a proton = 3- n = 3 — 2 = 1 .

Therefore, a proton can be represented as ‘uud’.

A neutron also has three quarks. Let there be n up quarks in a neutron.

Charge on a neutron due to n up quarks = (+2/3 e )n

Number of down quarks is  3-n ,and each having a charge of -1/3 e.

Charge on a neutron due to (3-n) down quarks = (-1/3e) (3-n)

Total charge on a neutron =0

Therefore 0=(2/3 x e) n + (-1/3 x e) (3-n)

=>  0 = 2ne/3  –  e  +  ne/3

=> e= ne =>n=1

Number of up quarks in a neutron ,n=1

Number of down quarks in a neutron=3-n =2

Therefore, a neutron can be represented as ‘udd’.