### Video Transcript

Calculate the total number of down
quarks in the nucleus of an element that has atomic number nine knowing that its
nucleus contains 28 up quarks.

The atomic number is the number of
protons in the nucleus of an atom. It is the number of an element on
the periodic table. We’ve been told in the question
that the element has the atomic number nine. So, we can deduce that the nucleus
of this atom will contain nine protons. Quarks are subatomic particles with
fractional electric charges and are fundamental constituents of matter. There are six different types or
flavors of quark. They’re called up, down, charm,
strange, top, and bottom. They can combine in different ways
to form composite particles such as protons and neutrons. A proton is composed of two up
quarks, represented by the letter u, and one down quark, represented by the letter
d, whereas a neutron contains one up quark and two down quarks.

We’ve already worked out that we
have nine protons. If in one proton, we have two up
quarks, then in nine protons, we’ll have nine times two up quarks, which is 18 up
quarks. And if one proton contains one down
quark, then nine protons will contain nine times one down quark, which is nine down
quarks. We have been told in the question
that the nucleus contains 28 up quarks. We have calculated that 18 of these
come from the protons. And since the nucleus of an atom
only contains protons and neutrons, the remaining up quarks must come from the
neutrons.

To find the number of up quarks in
the neutrons, we need to subtract the number of up quarks in the protons from the
total number of up quarks. 28 up quarks minus 18 up quarks
equals 10 up quarks. As in a neutron, there is one up
quark for every two down quarks, then for every 10 up quarks, there must be two
times 10 down quarks, which is 20 down quarks. So, we have calculated the number
of down quarks in the protons in this nucleus and the number of down quarks in the
neutrons.

So, to find the total number of
down quarks, we need to add the number of down quarks in the protons and the
neutrons. Nine down quarks plus 20 down
quarks equals 29 down quarks. Therefore, the total number of down
quarks in this nucleus is 29.