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 `(-1/3e)`, 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

Quark composition of proton : Suppose one proton is made up of `n_(1)` no. of up quark and `n_2` no. of down quark. Hence, Charge of one proton = `n_(1)` (charge of one up quark) +`n_2` (charge of one down quark)
`therefore e=n_(1) ((2e)/3) + n_(2) (-e/2)`..........(1)
But we are given that `n_(1) + n_(2) = 3`
`therefore n_(2) =3-n_(1)`.............(2)
From eqns. (1) and (2),
`e = n_(1) (2e)/3 + (3-n_(1)) (-e/3)`
`therefore e=(2n_(1)e)/3 - e + (n_(1)e)/3`
`therefore n_(1)e = 2e`
`therefore n_(1) -= 2`......(3)
From eqns. (2) and (3)
`n_(2) = 3-2`...........(4)
`therefore n_(2) =1`
Thus, one proton is made up of 2 up quarks and 1 down quark. Hence, quark composition of proton can be shown as "uud" where u = up quark and d = down quark.
Quark composition of one neutron : Suppose one neutron is made up of `n_(1)` no. of up quarks and `n_2` no. of down quarks. Hence, Charge of one neutron = `n_(1)` (charge of one up quark) + `n_2` (charge of one down quark)
`therefore O = n_(1) ((2e)/3) + n_(2) (-e/3)`...........(5)
But we are given that `n_(1) + n_(2) =3`
`therefore n_(2) = 3-n_(1)`........(6)
From eqn. (5) and (6)
`O = n_(1) ((2e)/3) + (3-n_(2)) (-e/3)`
`therefore n_(1) =1`...........(7)
From eqn. (6) and (7)
`n_(2) = 3-1`
`therefore n_(2) =2`...........(8)
Thus, one neutron is made up of 1 up quark and 2 down quarks. Hence, quark composition of neutron can be shown as "udd".