# Why does copper have a weird atomic mass?

One of my students was scanning through a table of atomic weights and noticed that copper was odd because it has an atomic mass which isn't a whole number. Copper has a relative atomic mass of 63.55. I thought I'd share our discussion because it draws in a lot of interesting Physics and Chemistry.

# Isotopes

Copper is actually a mixture of different isotopes. Remember the chemistry of an atom is determined by the number of electrons it has. All solid elements have to be electrically neutral, otherwise their atoms would all have the same charge and the element would blow itself apart thanks to electric repulsion. Clearly, this doesn't happen. That means the number of positively charged protons in the nucleus has to be exactly equal to the number of negatively charged electrons in orbit around the nucleus. Copper has 29 protons in its nucleus, and that means it must have 29 electrons whizzing about outside the nucleus. But the number of neutrons can vary without affecting the chemistry of copper because neutrons don't have any charge.

Naturally occurring copper has two main ingredients: $${}^{63}_{29}Cu$$ and $${}^{65}_{29}Cu$$. That means its relative atomic mass depends on the proportions of these two isotopes. 69% of naturally occurring copper on Earth is the $${}^{63}_{29}Cu$$ variety and 31% is the $${}^{65}_{29}Cu$$ isotope. That means the overall atomic mass is a weighted average of the two:

$$\mbox{Copper Relative Atomic Mass}=0.6909 \times 62.9296 + 0.3091 \times 64.9278 = 63.55$$

In fact, if you look in detail copper is not that unusual in having an atomic mass which isn't even near a round number. To see this for yourself, take a look at the top-left hand corner for each element in the table below. So what is relative atomic mass and why is it useful?

## Counting & weighing atoms

In Chemistry we're usually interested in reactions between atoms and molecules, so an important thing is how many atoms and molecules we have. To understand why imagine we have to pair lots of gloves together. Gloves require a left hand and a right hand glove to make a pair.

• One left-hand glove + one right-hand glove = 1 pair of gloves
• Two left-hand gloves + two right-hand gloves = 2 pairs of gloves

But what if we had one thousand left-hand gloves and only one right hand glove? Well, we could only make one pair. The lack of right-hand gloves would be rate-limiting. In Chemistry we usually deal with weights of chemicals. If we had the weight of left-hand and right-hand gloves we would need to work out the pairs we could form in two steps

• Calculate number of left-hand gloves = weight of left-hand gloves / weight of one glove
• Calculate number of right-hand gloves = weight of right-hand gloves / weight of one glove

In case you don't remember what gloves look like here's a nice French 18th century pair made of silk. The left-hand glove is shown palm-upwards and the right hand one is palm downwards to show off the beautiful design to best effect.

The same idea applies if we are reacting hydrogen with oxygen to make water. We know that

$$\mbox{H}_2\mbox{O}$$

consists of two atoms of hydrogen for each atom of oxygen. If we wanted to make 5 water molecules we would need 10 hydrogen atoms and 5 oxygen atoms. What if we had 11 hydrogen atoms and 5 oxygen atoms? Well, we'd still only be able to make 5 water molecules and we'd have a spare hydrogen atom.

Relative to atoms we're big creatures, so big that we can only perceive millions of molecules at a time. So we need a standard number, a really big number, of molecules or atoms, to work with. That number is called a mole which is 602,214,085,700,000,000,000,000. That's 602 thousand billion, billion atoms or, in more compact scientific notation, that's 6.022140857x10^23. If you're wondering how that's defined, it's the number of carbon-12 atoms in 12 grams of carbon-12 which is the most abundant isotope of carbon. Relative atomic mass is the weight in grams of one mole of molecules or atoms or photons or gloves (a mole of 40g gloves would weigh 2.4x10^22 kg which is one third the weight of the Moon).

## Moles in action

If we want to make a litre of water how many molecules is that?

This is where relative atomic mass comes in. The relative atomic mass of water in grams is

$$\mbox{Water Relative Atomic Mass}= 2 \times 1.00794 + 15.999 = 18.01488$$

The weight of one mole of water is 18.01 grams. One litre of water weighs one kilogram, so that's

$$\mbox{Moles in 1 kg of Water}= \frac{1000}{18.01488} = 55.51$$

A kilogram of water is 55.51 moles of water molecules. The ingredients were 55.51 moles of oxygen atoms and 55.51 moles of diatomic hydrogen. If we count individual hydrogen atoms we would have twice as many, 111.02 moles.

So we know that naturally occurring copper is a mix of two isotopes, but why do we get this pair of isotopes, and where did it this copper come from?

Starting with the mixture of isotopes, there are two forces that balance one another when building atomic nuclei: electric forces and the strong force. All those positively charged protons packed together are trying to blow the nucleus apart. Counteracting this is the strong nuclear force that holds the nucleus together. Roughly speaking the two forces balance if the number of neutrons and protons is equal.

As the nucleus gets larger and electric repulsion between protons increases the mixture changes. In order for the strong force to balance electric repulsion the neutrons must outnumber the protons. In the graph below the black squares show the stable combinations of neutrons and protons and coloured squares are unstable isotopes. The straight and solid black line would mark nuclei where the number of neutrons and protons are equal but notice how the stable nuclei shift further above the line (have an excess of neutrons versus protons) as the nuclear mass increases. You can see that very few combinations are stable, most aren't and decay.

We think that the copper on Earth comes from bombardment by meteorites in its early stages of formation. These meteorites left over from the early solar system still fall and are collected and analysed and they have a similar ratio of 70% copper-63 to 30% copper-65 and this varies very little (by around a tenth of one percent). But that begs the question: where did the copper in those meteorites come from?

The elements that you see around you were forged in stars and blown out into space as those earlier generation of stars died. Here's a periodic table showing where the elements were forged (and this is a nice paper from 1957 by Burbidge, Burbidge, Fowler & Hoyle which summarises the processes, see page 552). You can see that the Big Bang was responsible for most of the matter in the universe: hydrogen and helium. But stars are the forges responsible for all the heavier elements, including the oxygen, carbon, nitrogen, calcium and phosphorus in our bodies.

For the billions of years of a star's life its core fuses hydrogen into helium and releases heat and light. We now think that copper was made in stars which are eight times or more the mass of the Sun as they used up their hydrogen fuel and became Red Supergiants. Elements form concentric shells around the core of these giant, dying stars and as fusion finally stops completely the star explodes as a supernova and blasts the shells and the newly forged elements into space.

It turns out that the first generation of stars that formed after the Big Bang didn't produce much copper at all. This is because in order to produce copper the star needs to form with iron from a previous supernova already contained in its structure. Then once the star ages the following reactions can happen:

• Fusion of helium-4 creates carbon-12 and capture of two protons produces nitrogen-14.
• Helium nuclei bombard nitrogen-14 to produce some neon-22.
• Neon-22 combines with more helium-4 to produce some magnesium-25 plus a neutron.
• Neutrons change iron-52 that is already present in the star into copper-63 and copper-65.

How do we know about this? It's largely thanks to spectroscopy which is the analysis of light from stars, supernovae and nebulae. This lets us work out which elements are present and their relative amounts even if they are thousands of light years away. The planetary nebulae that form when stars blow off the layers of synthesised elements into space are some of the most beautiful astronomical objects. Here's the Eskimo nebula (or clown nebula because it looks a bit like a clown) which has a double-shell structure which is in the constellation Gemini. This nebula started to form around 10,000 years ago and to give you some idea of its size those outer streamers are light years in length.

It turns out, then, that copper, like us, is made from stardust. Just as we shed our skin and this builds up as household dust over time, galaxies contain the shed skin of stars that have died. But unlike the elements in our bodies copper is special because it has been through the stellar forge twice, once as iron and then in its final form as copper. If we had evolved earlier in the existence of the universe we wouldn't have had so much copper which is such a critical element for modern electronics. So, as a species of electronic gadget-lovers, it's lucky we arrived once the nucleosynthesis party was in full swing.