### Video Transcript

The nucleus of a helium-4 atom
contains two protons and two neutrons. How many up quarks are in the
nucleus in total? How many down quarks are in the
nucleus in total?

Okay, so in this question, we’re
dealing with a helium-4 atom which we’ve been told consists of two protons and two
neutrons. Now, let’s start by recalling that
both protons and neutrons are made up of quarks, specifically up and down
quarks. A proton is made up of two up
quarks and one down quark, whereas a neutron is made up of one up quark and two down
quarks. So based on this information, we
can see that our helium-4 nucleus is made up of two protons, each of which contains
two up quarks and a down quark, and two neutrons, each of which contains two down
quarks and one up quark.

And now, all we have to do is to
add up the number of up quarks in this nucleus and down quarks in this nucleus
too. So let’s start with up quarks. Let’s say that the number of up
quarks is equal to the number of up quarks in a proton, which is two, multiplied by
the number of protons in the nucleus, which is two. And then to this we need to add the
number of up quarks in the neutrons. So each neutron contains one up
quark. And there are two neutrons in the
nucleus, one, two. And at that point, we’ve accounted
for all of the up quarks in the nucleus. So we just need to simplify the
right-hand side of this equation. We can, therefore, see that the
total number of up quarks in this nucleus is six. And we can confirm that by actually
counting them, one, two, three, four, five, and six. And hence, our answer to the first
part of the question is that there are six up quarks in the nucleus in total.

Moving on to the number of down
quarks in this nucleus then, we can say that this is equal to, firstly, the number
of down quarks in protons where each proton has one down quark in it and there are
two protons in the nucleus. And to this we need to add the
number of down quarks in the neutrons. Now each neutron has two down
quarks. And there are two neutrons in the
nucleus. And so when we evaluate the
right-hand side of this equation, we find that there are also six down quarks in
this nucleus. Let’s confirm that by counting,
one, two, three, four, five, and six. Hence, our answer to the second
part of the question is that there are six down quarks in the nucleus in total.