Home Board Paper Solutions Text Book Solutions Articles NCERT Exemplar Solutions
Question 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 = (2/3 e) n

Number of down quarks in a proton = 3 − n

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

Charge due to (3 − n) down quarks = (-1/3 e) (3-n)

Total charge on a proton = + e

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

⇒ e = 2ne/3 - e + ne/3

⇒ 2e = 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 = (- 1/3 e) (3-n)

Total charge on a neutron = 0

Therefore, 0 = (2/3 e) n + (-1/3 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’.

2 Comment(s) on this Question

Write a Comment:

• NCERT Chapter