Video: Deducing Which Unknown in a Table of Data on a Selection of Isotopes Has a Given Value

In the table below, which of the following has a value of 8?

04:27

Video Transcript

In the table below, which of the following has a value of eight?

At the far left of the table, we have a column called “Isotope of Atom.” An isotope is a type of atom. The letter or pair of letters in the symbol indicates the element and the number superscripted to the left is the mass number. So, we can read the first entry as isotope of fluorine with a mass number of 18. The mass number is simply the number of protons and neutrons that we would find in a nucleus of this particular isotope.

So, what we seem to have is a table that’s listing properties for four atoms, which are all different isotopes of different elements. The first entry is an atom of fluorine 18, the second atom is an atom of nitrogen 15, and the third atom is an atom of carbon 13. But for the fourth atom, although we know it’s an atom of potassium, we don’t know its mass number. It’s just been given the symbol D. So, it’s one of the unknowns that we need to figure out. So, what I’m going to do is walk through how to figure out what A B, C, D, and E are. And then, we’re going to find the one that has a value of eight.

So, here’s the question: How do we find out the number of protons in an atom of fluorine 18? We know the mass number of fluorine 18. It’s 18. And that’s the number of protons and neutrons in the nucleus. But we just want to know the number of protons. For that, we need the atomic number. Sometimes when nucleoid symbols like these isotopes symbols are written down, the atomic number is written in subscript to the bottom left of the element symbol. But in this question, they haven’t been so generous. We’re going to have to think of another way. Thankfully, we can look up the atomic number of an element on the periodic table.

For fluorine, the atomic number is nine, which means the number of protons in the atom of fluorine 18 we have here is nine. Unfortunately, nine isn’t eight. So, we have to continue our calculations. Now, since we figured out how to do atomic numbers, let’s do the atomic numbers for all the atoms and then come back to the calculations. The atomic number for nitrogen is seven. So, we figured out one more value. But unfortunately, it doesn’t have a value of eight. The atomic number for carbon is six. And the atomic number for potassium is 19. So, we could also fill in the number of protons for these atoms.

Now, let’s move on to figuring out the number of neutrons. We can easily figure out the number of neutrons by just taking the atomic number away from the mass number. Since the mass number is the number of protons and neutrons, all we need to do is take away the number of protons to get the number of neutrons. So, there are nine neutrons in our atom of fluorine 18. We just take the mass number, 18, and take away the atomic number, nine. And the number of neutrons for our atom of nitrogen 15 is eight, 15 minus seven. So, we found our answer. But I’m gonna fill in the rest of the table anyway. It’s just good practice.

13 minus six is seven. So, there are seven neutrons in our atom of carbon 13. And we can move on to figuring out the number of electrons. Now, we’ve been told we’re dealing with atoms. And atoms are by definition neutral. So, they have the same number of protons and electrons. And we can see that in the example of our potassium isotope. So, C is six because we have six electrons in our atom of carbon 13. We have seven electrons in our nitrogen atom. And there are nine electrons in our atom of fluorine 18. To figure out the last entry in the table, which is the mass number for our potassium isotope, all we need to do is add up the number of protons and the number of neutrons, meaning that our final unknown has a value of 40.

And our final selection with a value of eight is the number of neutrons in an atom of nitrogen 15.

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