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# 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

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 + $\left ( \frac{2}{3} \right )$ e, and the ‘down’ quark (denoted by d) of charge $\left (- \frac{1}{3} \right )$ 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.

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Given, a proton and a neutron consist of three quarks each.

And, ‘up’ quark is of charge + $\left ( \frac{2}{3} \right )$ e, and the ‘down’ quark of charge $\left (- \frac{1}{3} \right )$ e

Let the number of 'up' quarks be n. Therefore, the number of 'down' quarks is (3-n).

$\therefore$ The net charge = $\\ n\times\frac{2}{3}e + (3-n)\frac{-1}{3}e = (n-1)e$

Now, A proton has a charge +1e

$\therefore$ $(n-1)e = +1e \implies n =2$

Proton will have 2 u and 1 d, i.e, uud

Similarly, neutron has a charge 0

$\therefore$ $(n-1)e = 0 \implies n =1$

Neutron will have 1 u and 2 d, i.e, udd

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