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’.
