#### Question

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.

#### Solution

A proton has three quarks. Let there be *n* up quarks in a proton, each having a charge of `+2/3e`.

Charge due to *n *up quarks`=(2/3e)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 `=(-1/3e)(3-n)`

Total charge on a proton = + *e*

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

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

`2e= n e`

`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 `=(+3/2e)n`

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 = `(-1/3e)(3-n)`

Total charge on a neutron = 0

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

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

`e=n e`

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’.