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.

Answer 1

It is now believed that protons and neutrons (which constitute nuclei of ordinary matter) are themselves built out of more elementary units called quarks.

Answer 2

Answer:

A neutron can be represented as 'udd'.

Explanation:

A proton has three quarks. Let there be n up quarks in a proton, each having a charge of

$\large \:+ \:( \frac{2}{3} \:e \:)$

Charge due to n up quarks

$\large \:= \:( \frac{2}{3} \:e \:) \:n$

Number of down quarks in a proton = $\large \:3 \:- \:n$

Each down quarks has a charge of

$\large \:- \frac{1}{3} \:e$

Charge due to ( 3 - n ) down quarks

$\large \:= \:( \:- \frac{1}{3} \:e \:) \:( \:3 \:- \:n \:)$

Total charge a proton = +e

Therefore,

$\large \:e \:= \:( \frac{2}{3} \:e \:) \:n \:+ \:( \:- \frac{1}{3} \:e \:) \:( \:3 \:- \:n \:)$

$\large \:e \:= \:( \frac{2ne}{3} \:) \:- \:e \:+ \frac{ne}{3}$

$\large \:2e \:= \:ne$

$\large \:n \:= \:2$

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 auarks. Let there be n up quarks in a neutron, each having a charge of

$\large \:+ \frac{2}{3} \:e$

Charge on a neutron due to n up quarks

$\large \:= \:( \:+ \frac{3}{2} \:e \:) \:n$

Number of down quarks is 3 - n, each having a charge of

$\large \:= \:( \:- \frac{3}{2} \:) \:e$

Charge on a neutron due to

$\large \:( \:3 \:- \:n \:)$

Down quarks =

$\large \:( \:- \frac{1}{3} \:e \:) \:( \:3 \:- \:n \:)$

Total charge on a neutron = 0

$\large \:0 \:= \:( \frac{2}{3} \:e \:) \:n \:+ \:( \:- \frac{1}{3} \:e \:) \:( \:3 \:- \:n \:)$

$\large \:0 \:= \frac{2}{3} \:en \:- \:e \:+ \frac{ne}{3}$

$\large \:e \:= \:ne$

$\large \:n \:= \:1$

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'.