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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 (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.

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#### Solution

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 `-1/3"e"`.

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

Total charge on a proton = + e

∴ `"e" = (2/3"e")"n" + (-1/3"e")(3 - "n")`

`"e" = ((2"ne")/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, each having a charge of `+3/2"e"`.

Charge on a neutron due to n up quarks = `(+3/2"e")"n"`

The number of down quarks is 3 − n, 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

`0 = (2/3"e")"n" + (-1/3"e")(3 - "n")`

`0 = 2/3 "en" -"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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