2021 A/L Physics Past Paper · Question 08 (English Medium)

Answer: (3) $-\dfrac{1}{3}e$

What the question asks

What we know:

A proton and a neutron are each made of three tiny particles called quarks. There are two kinds here: up quarks, $u$, and down quarks, $d$.

What each letter means:

$e$ ($\text{C}$): the elementary charge, the charge of one proton.

$q_u$ ($\text{C}$): the charge of one up quark.

$q_d$ ($\text{C}$): the charge of one down quark.

We want: the charge of one down quark, $q_d$.

The plan: a proton is two up quarks and one down quark. We know the proton's charge and the up quark's charge. What is left over is the down quark.

Relevant theory

There are two types of fermions. They are leptons and quarks. The electron belongs to the fermion category while the proton and neutron are a combination of three quarks. An important property of quark particles is that the magnitude of their charge is 1/3 or 2/3 of the charge of an electron.

The proton is made up of two u quark particles of charge +2/3 and one d quark particles of charge -1/3.

The neutron is a neutral particle without any charge.

Reading the options

Think of three coins in a bag. You know the bag holds $1$ rupee in all. Two of the coins are the same kind. If you know those two, you can find the third.

The proton is the bag. It holds $+e$ in all. It has two up quarks and one down quark.

Add the three charges of the proton:

$$q_u + q_u + q_d = +e$$

This says: the charges of the three quarks add up to the charge of the proton.

$+\dfrac{4}{3}e$

$2 \times \left(+\dfrac{2}{3}e\right)$

$-\dfrac{1}{3}e$

$q_d = e - \dfrac{4}{3}e$

The two up quarks give a bit too much, $\dfrac{4}{3}e$. So the down quark must take away $\dfrac{1}{3}e$.

That is why its charge is negative: $-\dfrac{1}{3}e$. It is option (3).

Why the other options fail

$+e$ is the charge of the whole proton, not of one quark.

$+\dfrac{2}{3}e$ is the charge of the up quark.

With $-\dfrac{2}{3}e$, the proton would have only $+\dfrac{2}{3}e$.

$-e$ is the charge of an electron. A quark has one third or two thirds of $e$.

Conclusion

Does it make sense?

A neutron is one up quark and two down quarks. Add them: $\dfrac{2}{3}e - \dfrac{1}{3}e - \dfrac{1}{3}e = 0$.

A neutron has no charge. So $-\dfrac{1}{3}e$ fits the neutron too.

$q_d = -\dfrac{1}{3}e$

A proton is two up quarks and one down quark, and its charge is $+e$. Two up quarks give $+\dfrac{4}{3}e$.

So the down quark is $e - \dfrac{4}{3}e = -\dfrac{1}{3}e$. The answer is (3).

Remember the proton as $u\,u\,d$ and the neutron as $u\,d\,d$. Up is $+\dfrac{2}{3}e$ and down is $-\dfrac{1}{3}e$.

Check: $u\,u\,d$ adds to $+e$, and $u\,d\,d$ adds to $0$.

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