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Question Video: Calculating the Number of down Quarks in a Nucleus Chemistry

Calculate the total number of down quarks in the nucleus of an element that has atomic number 9 knowing that its nucleus contains 28 up quarks.

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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.

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