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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.

Answer

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’.

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