## Tuesday, February 11, 2014

### History of the Periodic Table Part 2: What is Atomic Mass?

In the early 1800's, as Johan Wolfgang Dobereiner's triadic version of the periodic table was being developed, John Dalton, Thomas Thomson and Jons Jakob Berzelius were beginning to figure out the relative atomic masses of the elements. At the time, each element's mass was taken as a number relative to the lightest known element, hydrogen, which they called number 1. The logic behind this is that scientists believed that each element was built up of atoms of hydrogen. And at this time, knowing nothing about subatomic particles, they considered each atom to be an indivisible unit.

This relative mass idea is known as Prout's hypothesis. Scientists thought that the atomic mass of any element would always be an exact whole-number multiple of hydrogen's mass (1), but soon, to the shock of the scientists involved, this was proved to be wrong. Some measured masses weren't even close. In 1826, Berzelius (shown below right), a man devoted to careful measurement and fastidious lab work, developed a precise way to measure atomic mass through experiment.

He discovered that the atomic mass of chlorine, in particular, fell in between two whole numbers (its mass is approximately 35.45 u). In his Treatise on Chemistry, Berzelius described his procedure for measuring the atomic mass of chlorine:

"I established its [chlorine's] atomic weight by the following experiments: (1) From the dry distillation of 100 parts of anhydrous potassium chlorate, 38.15 parts of oxygen are given off and 60.85 parts of potassium chloride remain behind. (Good agreement between the results of four measurements.) (2) From 100 parts of potassium chloride 192.4 parts of silver chloride can be obtained. (3) From 100 parts of silver 132.175 parts of silver chloride can be obtained. If we assume that chloric acid is composed of 2 Cl and 5 O, then according to these data 1 atom of chlorine is 221.36. If we calculate from the density obtained by Lussac, the chlorine atom is 220 [relative to the atomic weight of oxygen]. If it is calculated on the basis of hydrogen then it is 17.735."

Notice that his measurement is almost exactly half of the modern measurement. The reason is that at the time scientists didn't know hydrogen existed as a diatomic gas so his hydrogen standard was off by half.

Atomic mass can be a confusing concept. Measured in unified atomic mass units, amu or just u, it is sometimes called atomic weight instead - the two terms are often used interchangeably, and most of the time that's fine. However, these are two of several terms in chemistry that create a lot of problems for students and wreak havoc on their teachers. Chemwiki has an excellent definition chart you can use to clear up the chaos. Strictly speaking, atomic mass is the mass of an individual atom at the microscopic scale, whereas atomic weight is the average atomic mass of an element. Isotopes are the reason why there is a subtle difference between the two definitions.

The Discovery of Isotopes: The Modern Atom Begins to Take Shape

Berzelius didn't know this, and in fact most high school chemistry students don't know this (yet), but you can measure the atomic mass of one sample of pure chlorine to fantastic precision and measure another sample of pure chlorine taken from somewhere else in the world and get a different number. Why?

Almost a century after Berzelius's work, around 1910, isotopes were discovered, and the unexpected discrepancies between measurements like the chlorine example I just mentioned, were shown to be due to an isotope effect, where the masses of elements may reflect a mixture of stable isotopes of those elements. This means that atoms of the same element (same number of protons) can have different numbers of neutrons in the nucleus, and that variation affects the atom's mass.

Most people credit the discovery of radioactivity to Henri Becquerel in 1896. He noticed that uranium salts blackened photographic plates, due to some kind of radiation, thought at first to be X-rays. It was not long until researchers such as Ernest Rutherford, Paul Villard and Pierre and Marie Curie realized that the radiation that Becquerel detected was more complex than first thought. And the implications were unsettling.

Around this time, researchers working with thorium, a radioactive element found in naturally occurring thorite minerals, discovered that the naturally found thorium in the mineral emits beta particles (electrons). A thin sheet of thorium in argon is shown below. Pure thorium is a silvery white lustrous metal but when some thorium oxide is present, as it usually is, it eventually tarnishes to black.

 alchemist-hp;Wikipedia
They found that thorium isolated from decaying uranium emitted an entirely different particle - the alpha particle. Thorium has over 30 (all radioactive) isotopes, most of which decay by emitting an alpha particle but some isotopes decay through beta decay.

They didn't know what alpha and beta particles were but they could detect that they moved in opposite directions when placed in an electric or magnetic field, and they could detect that one kind (beta) always traveled a lot further than the other kind (alpha). It only took a few years for Becquerel to realize that the beta particle was an electron based on its mass to charge ratio, which was the same as Thomson's results. Otherwise, the two thorium samples were identical. These results flew directly in face of Dalton's atomic theory: If two atoms have the same number of electrons they must also have the same number of protons in their nuclei, and therefore they should behave identically. And yet, these researchers knew that something had to be different between these two thorium samples.

There are many different kinds of radioactive decay and some of them change or transmute one kind of atom into another kind by changing a neutron into a proton or vice versa. Protons were discovered in 1917 when Rutherford expanded on Prout's idea that hydrogen was a standard building block of all heavier elements. Hydrogen contained only one of the newly discovered positively charged particles  emitted through some kinds of radiation (proton emission), while other atoms contained more of these particles. Rutherford named these positive particles protons in 1920.

Along with the isotope mystery, something about atoms was way off. Scientists, looking at the various elements, knew that the relative atomic mass of an atom always seemed to be a bit more than double the atomic number, Z. They also knew that almost all the mass of an atom was concentrated in a tiny volume in the centre (thanks to Rutherford). The atom, as far as they knew,  consisted only of protons and electrons and the atomic mass data meant there had to be twice as many protons as electrons. This was a mystery because they also knew that atoms are electrically neutral. They thought that perhaps half the electrons were bound up in with the protons, cancelling their positive charge somehow. It wasn't a very satisfactory explanation, and the newly formulated uncertainty principle implied that there wasn't nearly enough energy in the atom to confine the (electrically repulsive) electrons inside the positive nucleus.

Neutrons were discovered in 1932 by James Chadwick. It's a bit of a story and the link explains how he did it. His discovery of the neutron finally put the lingering isotope mystery on firm conceptual ground. Isotopes have the same number of protons but different numbers of neutrons in their nuclei. The alpha particle was finally found to be a helium nucleus, consisting of two protons and two neutrons.

Relative atomic mass, which used to be called standard atomic weight, is now calculated as 1/12 the mass of carbon-12. Carbon-12 has an exact isotopic mass of 12 u. This exact value is what makes it useful as a standard atomic mass. Carbon as looked up on Wikipedia has a mass of 12.0107 u and this difference reflects the fact the it is the average mass of carbon-12 and carbon-13, two stable isotopes, according to their average natural abundance.

However, the isotopic makeup of samples from different sources on Earth can vary quite a bit, and this turns out to be both a little problem and a very useful scientific tool. On the plus side, you can pinpoint the original location of archeological samples of bone, teeth, iron tools, glass and lead-based pigments based on their isotopic profile. On the minus side, this can lead to inaccuracy when relying on the relative or average value for mass. Calculating the geographical variance of the isotopic profile for various elements is still a work in progress, as scientists work out with increasing precision the relative isotopic abundance of elements not just at various locations on Earth, but in the universe as a whole.

As a result, in 2010 the International Union of Pure and Applied Chemistry (IUPAC) changed the formal definition of atomic mass. The atomic masses of hydrogen, lithium, boron, carbon, nitrogen, oxygen, silicon, sulfur, chlorine and thallium are now written as intervals rather than as single numbers. Some modern applications require very precise atomic mass, so this change is necessary for accuracy. *Carbon is now listed as 12.0107 +/- 0.0008 u, a reflection of the varying abundance of two stable isotopes - carbon-12 and carbon-13 depending on the geographical origin of the sample. Only ten elements have so far been updated either because others only exist as a single stable isotope or because the upper and lower mass limits of the element haven't been measured yet. The IUPAC also regularly updates atomic masses as measuring precision improves.

Below is a screenshot from Wikipedia showing the average relative atomic masses of the elements. It doesn't reflect the new mass intervals of ten elements.

Lead (Pb, Z=82, atomic weight = 207.2) is the heaviest stable element. All elements with atomic numbers over 82 have no stable isotopes. The atomic mass of these elements is taken as the mass of the longest-lived isotope, and for some very short-lived elements it is an estimate only.

Mass Defect

When isotopes were discovered, scientists figured that a pure isotope (no mixture) should still have a relative atomic mass that is an exact multiple of 1 to within 1%. In other words, it should have a mass equal to adding up the individual masses of its protons, neutrons and electrons (proton and neutron masses are almost identical). However, this too is now known to be incorrect, and we will use the element helium as an example to explain why.

Helium exists almost entirely as helium-4 on Earth. Based on what we now know about relative atomic mass, we expect its mass to be almost exactly 4.000 - 2 neutrons + 2 protons = 4 (plus a small mass contribution made by electrons). We find by Googling helium that its average measured atomic mass (standard atomic weight) is 4.003.

However, helium-3 is also present in trace amounts on Earth (it is the only other stable isotope of helium). Looking up helium-3, we find it has an isotope mass of 3.016. Wait a minute. We expect it to be almost exactly 3.000 because it is a pure isotope. Why so much off?

This leaves us with two questions: (1) why isn't helium-3, a single isotope, almost exactly 3.000 and (2) why is the average atomic mass of helium slightly HIGHER than 4.000 (4.003) rather than lower, since helium-3 (smaller mass) makes an, albeit, small contribution?

The answer is called mass defect. To illustrate what mass defect is, let's add up the known masses of all the subatomic particles in an atom of helium-4. It has two electrons, two protons and two neutrons. The masses of these particles (in amu) are all known to at least six significant digits so:

2 X proton (1.007276) = 2.014552
2 X neutron (1.008665) = 2.017330
2 X electron (0.000549 = 0.001098

Total = 4.032980

Why isn't this value 4.003, the measured mass of helium? First, let's recap what we know: 4.000 is helium's relative atomic mass (relative to carbon) but it is not its unified atomic mass, the value that reflects its actual average measured atomic mass as it is found on Earth. If we look up helium-4's unified atomic mass, it is 4.002603 amu (or just u), rounded up to 4.003 as shown above. This number is quite a bit different from both its relative atomic mass (4.000) and the value we got by adding up its components (4.032980).

The difference between the sum of the components and the measured amu value is called the mass defect. Energy is released when the helium nucleus is assembled from its protons, neutrons and electrons, so the helium atom has lower potential energy (reflected by 4.003 rather than 4.033). The mass difference, 0.030377 u, is the mass equivalent of the energy that is released. This released energy is called the binding energy. The helium nucleus has lower potential energy than it's separate nucleons but it has higher binding energy, and this is what makes the formation of helium atoms thermodynamically favourable. If we wanted to split a helium-4 atom, we would have to add that energy back.

You might wonder why we have to add energy to helium to get it to break apart. After all, doesn't the fission going on in nuclear plants release energy? The answer is in the size of the atom. Iron is the most stable atom of all atoms. It has the highest binding energy and therefore it doesn't fuse or split. Atoms smaller than iron release energy when they fuse into larger atoms. The larger atom will have higher binding energy and lower potential energy. Atoms larger than iron (including those used in nuclear fission reactions, such as uranium) release energy when they are split apart.

If we add up the components of helium-3, we get:

2 X proton (1.007276) = 2.014552
1 X neutron (1.008665) = 1.008665
2 X electron (0.000549 = 0.001098

Total = 3.024315

Helium-3's isotopic mass is 3.0160293 u, so 3.024315 - 3.0160293 gives it a binging energy of 0.0082854 u, about a quarter of helium 4's binding energy of 0.030377 u.

ALL atoms, including those with radioactive unstable nuclei, have at least some positive binding energy. However, the binding energy in some atoms is not strong enough to hold the nucleus together indefinitely. These atoms will lose neutrons or protons (decay) until they reach a product that is stable. Very unstable nuclei may decay in microseconds while almost stable nuclei may take up to billions of years to decay.

The real measured atomic mass of an element therefore depends not only on its isotopic makeup but on its mass defect as well, and that depends on the particular atom's binding energy. An atom's binding energy consists of its nuclear binding energy (huge contribution since the strong force is involved) as well as its electron binding energy, better called ionization energy (a much smaller contribution since the far weaker electromagnetic force is involved). Ionization energy is the energy required to strip the atom of its electrons, to ionize it in other words.

Atoms with especially stable arrangements of neutrons and protons have especially high mass defects, especially low potential energy, and especially high binding energy. Atoms with unstable nuclear arrangements are radioactive. Calculating stability compared to decay rate is a bit complicated; it is an example of a many-body problem in physics. Physics Stack Exchange provides a really good explanation of it, if you are curious. Radioactive nuclei will go through a decay process. There are three basic decay possibilities: A nucleus will change a proton into a neutron or the reverse (beta decay), it will eject either an alpha particle (helium nucleus) or a proton, or, third, it will eject an even larger element nucleus. These decays either result in a new isotope of the element (if only the number of neutrons is altered) or a whole new element (if the number of protons changes). The latter process is called transmutation and it is the only real way, along with fusion, to change one kind of element into another kind. This is the real-life version of the philosopher's stone mentioned in the previous article.

Helium, with its two neutrons, two protons and two electrons, forms an unusually stable atomic arrangement. The graph below compares binding energy with nuclear size.

Iron (Fe), mentioned earlier, has the highest binding energy (graph peak) while helium-4's binding energy forms an unusually sharp upward spike at the left end of the graph. Helium-4 has a remarkably stable nucleus giving it a significantly lowered atomic mass. If you look at helium-3 above you see that it's right in line of where it's supposed to be. It's nuclear arrangement of two protons and just one neutron gives it an average binding energy.

Helium is extremely inert, which means it is chemically unreactive under all normal conditions so it won't form any compounds. It is also almost always a monatomic gas, condensing to a liquid only at the very cold temperature of 4.22 K, or -269°C, that's very close to the temperature of the vacuum of outer space (2.73 K). Like all elements, these chemical properties of helium come from its electron configuration, which is influenced by the electron's interactions with each other and with the nucleus. Helium's unusually stable nucleus and high binding energy is why element formation in the early universe pretty much stopped after helium nuclei formed (all larger atomic nuclei have been created in stars).

Why isn't hydrogen chemically inert too? Iron, even though it has an extremely stable nucleus, is fairly chemically reactive. Because of its particular electron configuration, it can either lose or accept electrons (usually from water or oxygen) to form various ionic compounds, such as iron oxide (rust). It is the electron configuration, not nuclear stability, which influences the physical and chemical properties of the elements, aside from their radioactivity of course. Chemical bonds between atoms was explained by Gilbert Newton Lewis in 1916, as an interaction between the electrons of the atoms involved.

Between 1800 and the early 1900's, the idea of what an atom is evolved at an explosive rate because there were so many great minds at work on the concept of the atom. Around the same time as the proton and neutron were discovered, the electron configuration of the atom was being sorted out. Bohr's model of the atom hinted that electrons have specific energies within the atom. They can gain or lose only discrete packets or quanta of energy. In the 1920's the quantum mechanical model of the atom was formulated. The evolution from Rutherford's atomic model to the modern quantum mechanical model marks one of the greatest breakthroughs ever in both chemistry and physics, with spin-off progress in biology, engineering, geology, practically every other scientific discipline there is.

In 1817, when Johan Wolfgang Dobereiner was putting together his law of triads, none of these things were known - isotopes, nuclear binding energy and ionization energy. No one knew that mass and energy were equivalent. No one knew exactly how atoms interact with each other, why they give off light and other radiation and how they transmit heat. No one knew how the fundamental forces make atoms what they are. All they knew was that the Earth seemed to be composed of a growing list of various simple substances, substances that seemed at the time to be fundamental, meaning they can't be broken down into anything smaller, and that some substances reacted with other substances to make yet different substances and others did not react at all. Unknown to researchers of this time, they were taking the first steps toward an amazing new era of science.

Next up: History of the Periodic Table Part 3.

1. A very comprehensive and well written account of the development of the periodic table and the structure of the atom.

Two brief comments if I may. There may be a small error in the weight given above for the mass of the carbon-12 isotope. It should read exactly 12.000 atomic mass units, not almost exactly 12.

Secondly, I wonder whether one can really speak of Dobereiner's triads as constituting a periodic table as such. The discovery of triads is certainly an anticipation of periodicity but Dobereiner failed to connect triads together into any form of 2-dimensional array or 'table'.

please see www.ericscerri.com for further information and resources on the periodic table.

1. Thank you, Dr. Scerri!

Here's the mistake in my original text:

"Relative atomic mass, which used to be called standard atomic weight, is now calculated as 1/12 the mass of carbon-12 (which happens to be almost exactly 12 u; 12.0107 u to be more exact*). It is the average atomic mass of both stable isotopes of the element carbon (carbon-12 and carbon-13) based on their relative abundance on Earth.

This is how it reads now in the text:

Carbon-12 has an exact isotopic mass of 12 u. This exact value is what makes it useful as a standard atomic mass. Carbon as looked up on Wikipedia has a mass of 12.0107 u and this difference reflects the fact the it is the average mass of carbon-12 and carbon-13, two stable isotopes, according to their average natural abundance.

Secondly, Dobreiner's triads should instead by described as a first attempt to find relationships between elements, but Dr. Scerri correctly points out they were not connected together yet in any kind of table.

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