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Average atomic mass

The average atomic mass (sometimes called atomic weight) of an element is the weighted average mass of the atoms in a naturally occurring sample of the element. Average masses are generally expressed in unified atomic mass units (u), where 1 u is equal to exactly one-twelfth the mass of a neutral atom of carbon-12. Created by Sal Khan.

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  • boggle blue style avatar for user Kalshi
    So the atomic mass unit is 1/12th the mass of carbon-12. And the average atomic mass of hydrogen is approximately 1 relative to this value. So, wouldn't one atom of hydrogen be more ideal for the amu, especially when finding the relative atomic mass? So I'm just wondering why it had to be 1/12th of carbon??
    (40 votes)
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    • old spice man blue style avatar for user Victoria  Liu
      Good question that requires a kind of long explanation!

      A long time ago, the standard for measuring average atomic mass was actually based on oxygen, and scientists thought all oxygen was oxygen-16 (8 protons, 8 neutrons). But after isotopes were discovered (oxygen-17, oxygen-18, etc), everything got really confusing, so scientists agreed to use carbon-12.

      The average atomic mass for hydrogen is actually around 1.008 amu. Protium is by far the must abundant isotope of hydrogen, and it only contains 1 proton, and no neutrons. The relative abundance of Deutrium (1 proton, 1 neutron) is so small that it is barely accounted for when calculating the average atomic mass. So the mass of a proton is around 1.008 amu, not 1. Following this logic, the carbon-12 atom's atomic mass should actually be 12.09 amu; however, the mass is exactly 12 amu. Why?

      The missing mass is called mass defect, and it represents the binding energy. Since the nucleus is full of protons, which has positive charge, they would repel and the nucleus would fly apart. Binding energy is the energy that holds the nucleus together. Because of energy-mass equivalence (E = mc^2), we know that energy and mass are interchangeable. Some of the mass of the atom gets converted into binding energy, so the mass of the entire nucleus would actually be less than the mass of each individual proton and neutron added together. This is why the mass of carbon-12 is 12 amu, not 12.09.

      Scientists used carbon-12 because no other atom has exact whole-number masses in the amu scale. Also, scientists needed a pure isotope to base the system on.
      (142 votes)
  • duskpin tree style avatar for user SunnyWolf
    Hi! Here are some brief notes that I took in the video. If I got anything wrong, feel free to comment below (I would appreciate it)!

    Atomic mass unit (or "amu") - also known as "u", or "unified atomic mass unit".
    ★ u = 1.660540*10^-27kg (I know... what a number!)

    Proton - about 1 u (more closely, 1.007)
    Neutron - 1 u (more closely, 1.008)
    Electron - almost one two thousandth of a proton or neutron (in other words, really small!)

    ★ The number under the elements in the periodic table (for example, the "1.008" in Hydrogen) is the "aam", or average atomic mass.

    Average atomic mass - weighted average of various versions of the element (ex. 1.008 is the aam of Hydrogen).

    Isotopes - same element w/ different # of neutrons.

    My question: How many "versions" are there for each element? Is there an infinite # of versions? And if so, how do you calculate that average (aam)?
    Edit: Actually, the next video goes into calculating the aam. But I'm still wondering about how many versions there can be for an element.

    I hope this helps! Wherever you are in the world, I wish you luck in chemistry and whatever courses you will be taking in the future!
    (75 votes)
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    • starky sapling style avatar for user sahithigorthi
      I am assuming that when you say versions, you mean the various isotopes of an element? In that case, there aren't an infinite amount of versions; there is a set amount. I'm pretty sure there are some elements with ~36 isotopes, and there probably is more to discover. But there definitely isn't an infinite amount. As for the average atomic mass, we only are able to calculate it based on the isotopes that we know. Hopefully this helps and if I missed anything, feel free to add :)
      (16 votes)
  • aqualine ultimate style avatar for user Dr. Meyana
    What does it mean to say Carbon-12's neutron has 1.008amu? Since an amu is 1.660540*10^-27, does that mean that C-12's neutron is equal to 1.008*1.660540*10^-12? I don't really understand the math.
    (24 votes)
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    • mr pants purple style avatar for user Ryan W
      I don’t think that’s how you should be thinking about this. A carbon-12 atom has a mass of exactly 12 unified atomic mass units.
      Protons and neutrons in an atom have less mass than if they are unbound, the difference is called mass defect.
      (40 votes)
  • eggleston blue style avatar for user K.M Ahnaf Zamil
    At you said that a proton's mass is 1.007 u_ but when you showed the periodic table, the mass of Hydrogen was 1.008 _u. Isn't 1.008 u_ the mass of neutron? But Hydrogen doesn't have a neutron. Then why is the mass of Hydrogen 1.008 when the mass of a protonis 1.007 _u?
    (9 votes)
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    • mr pants purple style avatar for user Ryan W
      The mass on the periodic table is the average mass of a hydrogen atom, taking into account its three natural isotopes.
      You can’t say “hydrogen doesn’t have a neutron” because two of its natural isotopes do, this pushes the average mass up ever so slightly.
      (21 votes)
  • blobby green style avatar for user Peter Patterson
    It's very useful to have the average masses of atoms on the periodic table, but how did we actually measure the mass of a neutron or a proton?
    (9 votes)
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    • leaf red style avatar for user Richard
      A proton's mass can be measured in a mass spectrometer which accelerates a proton through an electric field where it is deflected by a perpendicular magnetic field. The amount of deflection determines the mass of the charged particle. The more a particle is deflected, the less mass it has. We also use this method to determine the masses of molecules. Mass spectrometry only works on charged particles so only the proton's mass can be determined directly using this method since the neutron has no charge.

      For the neutron, an indirect method using mass spectrometry is utilized. A proton's mass can be determined, as can a deuterium's mass using mass spec. Deuterium is one of the less abundant isotopes of hydrogen which contains only 1 proton and 1 neutron. You can essentially find the difference in mass between the deuterium and proton to find the mass of the neutron. Hope that helps.
      (20 votes)
  • piceratops ultimate style avatar for user zakirahana
    How can 80%(5AU) + 205(6AU) be equal to 5.2 AUs?
    (4 votes)
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    • piceratops ultimate style avatar for user Kavi
      Because it's a weighted average. If 80% of the atoms are 5U and 20% of the atoms are 6U, in a sample of 100 atoms, roughly 80 of them will be 5U, and roughly 20 of them will be 6U. If you take the average of all those atoms (80*5 + 20*5)/100, you get 5.2.
      (17 votes)
  • leafers tree style avatar for user Lilianna
    Hello! I'm wondering why neutron's are larger than protons? Because protons are positive while neutrons are neutral, shouldn't protons be larger? I'm most likely thinking about this the wrong way, but does anyone know why they equal the amount that they do?
    (5 votes)
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    • duskpin ultimate style avatar for user W
      The slight difference in the masses of subatomic particles has to do with their composition. Protons and neutrons are made up of two types of fermions: UP and DOWN particles The UP particle has the properties: charge of 2/3 and mass of 2.2 V/c2. The DOWN particle has the properties: charge of -1/3 and mass of 4.7 V/c2. A proton is made of 2 UP and 1 DOWN, so its charge is 1. (add 2/3 to 2/3 to -1/3). A neutron is made of 1 UP and two DOWN particles, so it has a charge of 0. (add 2/3 to -1/3 to -1/3)

      BOTTOM LINE: Since DOWN particles are more massive and neutrons have more of them, neutrons are more massive than protons.
      (11 votes)
  • orange juice squid orange style avatar for user GMB2003
    I have a question. How was the atomic mass unit actually calculated and how was the specific 1.66×10^-27 kg number discovered. Also, how was the proton and neutron found to be close to this number? Thanks!
    (8 votes)
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    • piceratops sapling style avatar for user Yashojit Bhaumik
      Initially, the atomic mass was calculated taking 1 a.m.u. to be the mass of one hydrogen atom. But this method was not giving values as whole numbers or simple decimal numbers, extending to many decimal places which complicated calculations. Oxygen was used for a very brief period in place of hydrogen. Carbon was used since its abundantly available and gave whole numbers when used in place of hydrogen.
      (4 votes)
  • blobby green style avatar for user Vishal Jawa
    Why is the average 5.2 instead of 5.5?
    (5 votes)
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    • leaf red style avatar for user Richard
      It we wanted the arithmetic average then it would be 5.5 because (5+6)/2 = 5.5. But for average atomic mass we're calculating a weighted average. The difference between the two types of averages is that an arithmetic average are of equal importance, but a weighted average takes into account the importance of some values over others. For average atomic mass, the isotopes of an element are found in difference abundances or amounts in nature. This means that certain isotope's atomic masses contribute more to the element's average mass than other isotopes.

      For the hypothetical element Sal is describing, 80% of the element's atoms have an atomic mass of 5 amu, while only 20% have an atomic mass of 6. For this calculation we multiply the masses by their percentages and sum them up to find the weighted average. Keep in mind for percentages to be used in a calculation like this they need to be in decimal form. So 80% is 0.80 and 20% is 0.20. This means the calculation is: 5(0.80) + 6(0.20) = 5.2 amu.

      Hope that helps.
      (6 votes)
  • purple pi purple style avatar for user Maitreyee Majumder
    well then what is the number exactly which is displayed just below the elements in the periodic table?
    (4 votes)
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    • leaf red style avatar for user Richard
      Technically they are relative atomic masses. Relative atomic mass is almost identical to average atomic mass. They both try to average the masses of the different isotopes of a single element to arrive at an average mass for an atom of that element. The difference is the units. Average atomic mass is in unified atomic mass units, u, while relative atomic mass is unitless.

      Hope that helps.
      (8 votes)

Video transcript

- [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.