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.

Explanation

For the protons, the charge on it is +e let the number of up quarks are a, then the number of down quarks are (3-a) as the total number of quarks are 3.
So, `a_(x)` up quark charge `+(3 -a )` down quark charge `=+e`
`a xx 2/3 e +(3-a) ((-e)/3)=e`
`(2a e)/3 -((3-a)e)/3=e`
`2a-3+a=3`
`3a=6`
`a=2`
Thus, in the proton there are two up quarks and one down quark.
`:.` Possible quark composition for proton = uud
For the neutron, the charge on neutron is 0.
Let the number of up quarks are b and the number of down quarks are (3-b)
So, `b_(x)` up quark charge `+(3-b) xx` down quark charge `=0`
`b((2e)/3)+(3-b)((-e)/3)=0`
`2b-3+b=0`
`3b=3`
`:. b=1`
Thus, in neutron, there are one up quark and two down quarks.
`:.` Possible quark composition for neutron = udd.