The nucleus of a carbon-14 atom contains six protons and eight 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’ve been told that in the nucleus of a carbon-14 atom, there’re six protons and eight neutrons. Now the first question asks us how many up quarks there are in the nucleus.
So to answer this question, we need to look deeper at these protons and neutrons. More specifically, we need to recall that protons and neutrons are made up of up and down quarks. And so we recall that a proton is made up of two up quarks, here’s one, here’s two, and one down quark. In other words then, we can say that a proton is equal to an up quark, an up quark, and a down quark combined together.
And similarly for a neutron, we can remember that this time there’s only one up quark. And that there’re two down quarks. And hence, we can say that a neutron consists of one up quark and two down quarks.
Now coming back to our carbon-14 nucleus, we know that it consists of six protons and eight neutrons. So how many up quarks are there in total? Well, first of all, we’ve got six protons. And each proton has two up quarks in it. So all together in the protons, there are six times two or 12 up quarks.
And then we can consider the up quarks in the neutrons. So there’re eight neutrons. And each neutron has one up quark in it. Hence, there’re eight times one or eight up quarks in the neutrons. So then in the entire nucleus combined, there are 12 plus eight up quarks. Or in other words, there’re 20 up quarks.
So now that we’ve answered that, let’s look at the next question: “How many down quarks are in the nucleus in total?” Okay, so once again, we can do the same thing, but this time for the down quarks. Let’s consider first the down quarks in the protons in the nucleus. Now once again there’re six protons. And each proton has one down quark in it. So just in the protons, there’re six times one down quarks or, in other words, six down quarks.
And then looking at the neutrons, we know that there’re eight neutrons. And each neutron has two down quarks in it. Hence, there’re eight times two down quarks in the neutrons. And this is equal to 16. So the total number of down quarks in the nucleus is six plus 16, or, in other words, 22.
And therefore at this point, we have our answers. In a carbon-14 nucleus, which contains six protons and eight neutrons, there’re in total 20 up quarks and 22 down quarks.