### Video Transcript

What particles does an atom of calcium-35 consist of? (a) 20 protons, 15 electrons, 20 neutrons. (b) 35 protons, 20 electrons, 35 neutrons. (c) 20 protons, 20 electrons, 15 neutrons. (d) 15 protons, 20 electrons, 35 neutrons. (e) 15 protons, 15 electrons, 20 neutrons.

This question is about the subatomic particles that make up atoms. The three constituents of an atom are protons and neutrons, which form the nucleus, and electrons, which form a cloud surrounding the nucleus. The charge and, to a very good approximation, the mass of a particular atom come from summing up the charges and masses of the individual constituents, the protons, neutrons, and electrons, of that particular atom.

Neutrons have no charge. Protons and electrons have charges equal in magnitude, but opposite in sign. For many problems, the magnitude of this charge in, say, coulombs is not important, but rather it’s sufficient to say the charge on a single electron or the charge on a single proton. So, we’ll say that the magnitude of the charge of electrons and protons is one to make the bookkeeping easier. Where we know that when we say a charge of plus one or minus one, we really mean plus or minus a small fraction of a coulomb.

In a similar way, we’re often concerned with the mass of an atom in terms of the mass of a proton. So, again, we’ll call the mass of a proton one and understand that when we say a mass of one, what we really mean is some small fraction of a kilogram. When keeping account of mass this way, neutrons also have a mass of one and electrons have a mass of zero. Even though an electron has a mass of about one part in 2000 of that of a proton, and the neutron is slightly more massive than a proton by about the electron mass. The reason we ignore those two is because this method of assigning charge and mass is really just to make the accounting easier. And corrections on the scale of an electron’s mass don’t affect the final results.

Now that we understand the convention for assigning charge and mass to the constituents of an atom, let’s understand how to read an atomic symbol like the one in the question. An atomic symbol typically consists of up to four components. At the center of the atomic symbol is the alphabetic element symbol. Here, we’ve used Z, which isn’t the symbol for any element as a placeholder. If this were an atomic symbol for hydrogen, we would replace Z with H. If it were for argon, we would replace Z with Ar.

The element symbol is then surrounded by up to three numbers. In the bottom left is the atomic number. The atomic number is also sometimes represented by the symbol capital A or capital Z. The atomic number is the number of protons in the nucleus of the atom. This number also tells us what kind of element the atom is. For example, if the atomic number is one, then the atom is hydrogen. If the atomic number is 53, the atom is argon.

Knowing the element also tells us some of its chemical properties, like the fact that aluminum is a metal and krypton is a noble gas. Note that what element in atom is is determined solely by its atomic number, independent of how many neutrons or electrons it has.

To get information about the neutrons, we look to the top left number of the atomic symbol, the mass number. The mass number of an atom is its mass in terms of our convention before, where protons and neutrons have mass one and electrons have mass zero. Therefore, the mass number is also the number of protons plus the number of neutrons, since each proton and neutron contributes one to the total mass number.

This number not only represents the approximate mass of the atom, but also contains key information about its stability. For example, uranium with a mass number of 238 has a half-life of around four and a half billion years. Whereas uranium with a mass of number of 239 has a half-life of less than 30 minutes, even though both have the same atomic number, 92.

The last thing we need to know is how many electrons an atom has. This information is included in the number in the upper-right corner of the atomic symbol, the charge. The charge is the total charge on the atom contributed by the net sum of the protons and electrons using our convention that protons have a charge plus one and electrons have a charge minus one. This means we could find the charge by taking the number of protons in the atom and subtracting the number of electrons. So, an atom with two more protons than electrons has a charge of plus two because the number of protons minus the number of electrons is two.

Alternatively, we could say that each proton–electron pair has a net zero charge. And then, each additional proton adds positive one to the overall charge. Similarly, each electron would add a negative one to the overall charge. Let’s look at an example. Consider a hydrogen atom that’s lost its electron. The element is hydrogen, so it’s symbol is H. Hydrogen has one proton whose atomic number is one and no neutrons, so its mass number is also one. It’s lost its electron, so it has one proton and no electrons. So, its charge is plus one.

Now that we can read an atomic symbol, we’re ready to answer the question. Before we do that, let’s quickly note that if no charge is written in the atomic symbol, the atom is neutral. That is, its charge is zero. Let’s now extract the relevant information from the symbol in the question. The element of symbol is Ca, calcium, and the atomic number is 20. So, right after that, we know that the number of protons, the atomic number, is 20. We used the octothorpe to represent number and the subscript p to tell us that we’re talking about protons, just to save space.

The other number we have written in this symbol is 35, and 35 is the mass number. Remember that the mass number is the number of protons plus the number of neutrons. So, we can write number of protons plus number of neutrons equals 35, the mass number. But we know that the number of protons is 20 from the atomic number. So, let’s substitute that into our equation. So, we have 20 plus the number of neutrons is equal to 35. Now, subtract 20 from both sides. On the left-hand side, 20 minus 20 is zero, and we’re left with the number of neutrons. And on the right-hand side, 35 minus 20 is 15. So, the number of neutrons in this atom is 15.

Now, we just need the number of electrons. We’ll get this from the charge, which is the number located in the upper right of the atomic symbol. Our atomic symbol doesn’t include a number in the upper right, which means that the atom is neutral. In other words, its charge is zero. We can, therefore, write number of protons minus number of electrons is equal to zero. And again substituting in 20 for the number of protons, we get that 20 minus the number of electrons is zero, which means that the number of electrons must be 20 because 20 minus 20 is zero.

Note that the number of electrons is the same as the number of protons. This is generally true in neutral atoms. In neutral atoms, the charge on every electron cancels the charge on a corresponding proton. So, the total number of protons is the same as the total number of electrons. We now have all the information we’re looking for.

The particles that make up an atom of neutral calcium-35 are 20 protons, 20 electrons, and 15 neutrons. So, the correct answer is choice (c). We could have arrived at this answer without even considering the charge. Since choice (c) is the only answer choice with the correct number of protons and neutrons, which we figured out from the mass number and the atomic number.