Question

It is now believed that protons and neutrons (which constitute nucleiof ordinary matter) are themselves built out of more elementary unitscalled 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 othertypes have also been found which give rise to different unusualvarieties of matter.) Suggest a possible quark composition of aproton and neutron.

Answer 1

Given: The up quark has charge of ( +2 3 )e and the down quark has charge of ( −1 3 )e.

The charge due to n number of up quarks is given as,

q n u =( 2 3 e )n

Where, the number of quarks in a proton is n.

The number of quarks in a proton is three.

The number of down quarks in a proton is given as,

n ′ =3−n

The charge due to ( 3−n ) number of down quarks is given as,

q n d =( −1 3 e )( 3−n )

We know that the total charge on a proton is +e.

Total charge on a proton is given as,

e= q n d + q n u

By substituting the given values in the above equation, we get,

e=( 2 3 e )n+( −1 3 e )( 3−n ) 2e=ne n=2

Hence, the number of up quarks is 2 and the number of down quarks is ( 3−2 )=1.

Thus, the quark composition for proton is uud.

We know that the total charge on a neutron is zero.

Total charge on a neutron is given as,

0= q n d + q n u

By substituting the given values in the above equation, we get,

0=( 2 3 e )n+( −1 3 e )( 3−n ) =( 2 3 e )n+( e 3 )( n−3 ) e( n−1 )=0 n=1

Hence, the number of up quarks is 1 and the number of down quarks is ( 3−1 )=2.

Thus, the quark composition for a neutron is udd.