Average atomic mass

- [Instructor] The thing that I've always found amazing about chemistry, it's an entire field of science that we as human beings have developed to actually understand what is happening in an almost unimaginably small scale. In particular we're gonna be thinking about the atomic, and even the subatomic scale. And by looking at that scale we can then begin to understand the universe in which we live in, the scale in which we live in, and even be able to make predictions about what will happen, and make things that are useful for human beings. So if we're going to operate at this small of a scale, and we're gonna appreciate in a few seconds how small of a scale it is, we're going to have to have some units of measurement. And this video is going to focus on mass. How do we measure mass at such a small scale? Well to do that the chemistry community has historically used something called an atomic mass unit. I'll write it here, atomic, atomic mass unit, and it's historically denoted as AMU. And more recently, the more modern version of this is the unified atomic mass unit, that is denoted by just a U instead of an AMU. So how does a unified atomic mass unit connect to our units of mass that we might use on a larger scale like, say, grams or kilograms. Well, the unified atomic mass unit is defined as 1.660540 times 10 to the negative 27 kilograms. So when you see something like this, you might have a few reactions. Your first reaction, which would be an appropriate reaction, is that wow, 10 to the negative 27 power is very small. To appreciate it you could write it out, it would be zero point and then 26 zeros and then you would have one six six zero five four zero. So very, very, very small, really unimaginably small. We can only try to abstract it with things like mathematics. The other thing you might appreciate is this feels like a bit of a hairy number here, 1.660540, why did they define it that way? And the answer to your question is, this definition makes it a lot cleaner when we think about the mass of whether it's an atom or the constituents of an atom like a proton or a neutron. Roughly speaking the mass of a proton is approximately one unified atomic mass unit. The mass of a neutron is approximately one unified atomic mass unit. It actually turns out that a proton's a little bit more than one, it's about 1.007 atomic mass units, but it's approximately one. And the neutron is actually a little bit more than even a proton, it's 1.008 approximately unified atomic mass units. Now an electron's mass is actually far smaller than either of these, it's actually almost one two thousandth of a proton or a neutron, and so you can imagine an atom which is made up of protons and usually neutrons and electrons as well, the mass is mainly going to be the protons and neutrons in the nucleus. And so if you know the number of protons and neutrons in the nucleus, you're going to have a pretty good sense of its atomic mass. And you can see that indicated on a periodic table of elements which we have here. And we will study the periodic table of elements in a lot more detail in other videos. But you can see a couple of interesting elements. One, you have the abbreviation of a given element, H represents hydrogen. The number on top on this periodic table, that's the atomic number, and that tells you how many protons it has. And an element is defined by the number of protons. So any atom that has exactly one proton in its nucleus is going to be hydrogen by definition. Any atom that has exactly 20 protons in its nucleus is going to be calcium by definition. Any atom that has exactly 36 protons in its nucleus is going to be krypton by definition. So what would you expect the mass of a hydrogen atom to be? Pause this video and think about it. Well we know that all hydrogen atoms by definition have one proton, but it actually turns out there's different versions of hydrogen that can have different numbers of neutrons. Most of the hydrogen in the universe actually has zero neutrons, zero neutrons. There are versions that have one or two neutrons, but most, 99.98% roughly, of hydrogen in the universe has one proton, zero neutrons, and if it's a neutral hydrogen it's going to have one electron. And when we talk about versions of a given element there's a fancy word for it, they're called isotopes. And the different isotopes, they'll all have the same number of protons 'cause they're talking about the same element, but they'll have different numbers of neutrons. And so if this is the most common form of hydrogen. What do you think its mass is going to be? Well its mass is going to be essentially the mass of a proton plus an electron, and roughly speaking it's going to be the mass of a proton 'cause the mass of a proton's going to be so much larger than the mass of an electron. And so you would expect that its mass is approximately one unified atomic mass unit. Now if you were to precisely look at the mass of a proton and a electron, if you add them together, you actually get something that's a little bit closer to 1.008. And you actually see that right over here on the periodic table of elements. Now this number, although it is pretty close to the mass of the version of hydrogen that I just described, it's actually a weighted average of the various versions of hydrogen. It's just close to this version because this version represents most of the hydrogen that we actually see around us. If for example you had two versions of an element, some hypothetical element, and let's say that 80% of the element that we see is version one and version one has a mass of let's call it five atomic mass units, and then version two, it's the remainder, 20%, of what we observe of that element, it has an atomic mass of six atomic mass units. You would get a weighted average here of 5.2 unified atomic mass units. And that's actually how these numbers are calculated. They are not just the mass of one type of that element, they're a weighted average mass of the various isotopes, of the various types. And so this number on a periodic table of elements is known as the average atomic mass, average, average atomic atomic mass. Now in older chemistry books, and this is actually the case when I first learned chemistry, they call this number atomic weight. And I've always complained about it because it's really talking about mass and not weight. If you don't know the difference you'll learn that at some point in the future, and it's really talking about average atomic mass. Now I'll give you one little detail that might be useful to you. Sometimes you'll hear something called relative atomic mass. It actually turns out this periodic table of elements, because it does not write a little U after each of these numbers, it's essentially these number are unitless, so it's really talking about relative atomic mass. So it's saying, hey on average, for example, the mass of a carbon atom is going to be roughly 12 times that of, on average, the mass of a hydrogen atom. If they put the units here, then that would actually truly be average atomic mass. But for our purposes, as we go into chemistry, you can look at these numbers, and say okay, if oxygen has a relative atomic mass of 16, it's average atomic mass is going to be 16 unified atomic mass units. And as we will see in the future, this understanding of average atomic mass will prove to be very, very useful.