1.31 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 =(23e)n

Number of down quarks in a proton = 3 - n

Each down quark has a charge of 13e

Charge duc to (3-n) down quarks =(13e)(3n

Total charge on a proton = +e

e=(23e)n+(13e)(3n)e=2ne3e+ne32e=nen=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 =(+23e)n

Number of down quarks is 3 - n, and each having a charge of 13e.

Charge on a neutron due to 3- n) down quarks =(13e)(3n)

Total charge on a neutron = 0

0=(23e)n+(13e)(3n)0=2ne3e+ne3e=nen=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''.