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’ quarks (denoted by $u$ ) of charge $ + \dfrac{2}{3}e$ , and the down quarks (denoted by $d$ ) of charge $ - \dfrac{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

Hint:A quarks is a type of elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles known as hadrons, the most stable of which are protons and neutrons, the component of nuclei. All common matter is composed of up quarks and down quarks and electrons.

Complete step-by-step answer:In the question it is given that a proton and a neutron consist of three quarks each that is up quarks and down quarks, the charge of up quarks is $ + \dfrac{2}{3}e$ and the charge of down quarks is $ - \dfrac{1}{3}e$ . Let's find the possible quarks composition of a proton and neutron one by one.
Quarks composition of a proton, let there are $(x)$ number of up quarks,
Then, the number of down quarks is $(3 - n)$
We know the total charge of a proton is $( + e)$
 $\left( {\dfrac{2}{3}e} \right)n\, + \,\left( { - \dfrac{1}{3}e} \right)\,(3 - n)\, = \,( + e)$
On solving the above equation, we will get
$\dfrac{2}{3}en - e + \dfrac{{ne}}{3}\, = \,e$
$\left( {\dfrac{2}{3} + \dfrac{1}{3}} \right)ne\, = 2e$
$ne = 2e$

If we cancel from both side $( + e)$ we will get value of $n$
$n = 2$

We get the number of up quarks number is $2$ then we know that number of down quark is $(3 - n)$. On putting the value of we get the number of down quarks.
$Number\,of\,down\,quarks\, = \,(3 - n)$
$Number\,of\,down\,quarks\, = \,(3 - 2)$
  $Number\,of\,down\,quarks\, = \,1$

Therefore, the possible composition of a proton consists of two ‘up’ quarks and one ‘down’ quarks.

Now, the quarks composition of neutron, we know the charge of a neutron is $zero\,(0)$ , so
$\left( {\dfrac{2}{3}e} \right)n\, + \,\left( { - \dfrac{1}{3}e} \right)\,(3 - n)\, = \,0$
On solving the above equation, we get the value of $(n)$
$(n = 1)$

Then we know the number of down quarks is $(3 - n)$
$Number\,of\,down\,quarks\, = \,(3 - n)$
$Number\,of\,down\,quarks\, = \,(3 - 1)$
$Number\,of\,down\,quarks\, = \,2$

Therefore, the possible composition of a proton consists of one ‘up’ quarks and two ‘down’ quarks.

Note:It is to be noted that there are six types of quarks namely; up quarks, down quarks, charm quarks, strange quarks, top quarks and bottom quarks. Out of them up and down quarks have the lowest masses of all quarks. The heavier quarks rapidly change into the up and down quarks through a process of particle decay, the transformation from a higher mass to a state to a lower mass state. Due to this reason up and down quarks are generally stable.