Ncert Exercises & Solutions

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 $= (\frac{2}{3} e) n$

Number of down quarks in a proton = 3 - n

Each down quark has a charge of $- \frac{1}{3} e$

Charge duc to (3-n) down quarks $= (- \frac{1}{3} e) (3 - n$

Total charge on a proton = +e

$\begin{matrix} ∴ e = (\frac{2}{3} e) n + (- \frac{1}{3} e) (3 - n) \\ \Rightarrow e = \frac{2 n e}{3} - e + \frac{n e}{3} \Rightarrow 2 e = n e \Rightarrow n = 2 \end{matrix}$

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 $= (+ \frac{2}{3} e) n$

Number of down quarks is 3 - n, and each having a charge of $- \frac{1}{3} e$ .

Charge on a neutron due to 3- n) down quarks $= (- \frac{1}{3} e) (3 - n)$

Total charge on a neutron = 0

$\begin{array}{l} ∴ 0 = (\frac{2}{3} e) n + (- \frac{1}{3} e) (3 - n) \\ \Rightarrow 0 = \frac{2 n e}{3} - e + \frac{n e}{3} \Rightarrow e = n e \Rightarrow n = 1 \end{array}$

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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