Part 2 of our article, in which we hope to develop an understanding of atomic structure and the periodic table, from the beginning of secondary school/junior-high level, to first/second year undergraduate physics/chemistry, via one fictional conversation. Missed Part 1? Find it here. Sigrid has just asked Sally what the point of an electron is…
SALLY: Well, where do we start? I mean, whereas protons and neutrons give an atom almost all its mass, the electrons give it almost all its size. And the number of electrons also pretty much determines all its chemical properties.
SIGRID: So the number of protons determines what element it is, and the number of electrons matches it. The number of electrons determines the chemistry. Seems to me that electrons are more important – why don’t they determine the element?
SALLY: Because atoms can lose or gain electrons to become ions, and then their number of electrons changes. But the ion is still an ion of the original element, because the protons are securely locked in the nucleus – and their number never changes. Well, unless it’s radioactive, but that’s a whole different conversation (or go here for a shortcut).
SIGRID: Oh OK, so in this book I have it says that the atomic number of an element (Z) is the number of protons. I guess that’s what you’ve just told me. And I guess this has something to do with why the periodic table is this funny shape and not just a rectangle.
SALLY: Yes – in the periodic table the elements are arranged in order of atomic number (number of protons) from left to right, but the rows are arranged so that related elements are placed into columns.
SIGRID: But when Mendeleev made the periodic table protons, neutrons and electrons hadn’t even been discovered yet.
SALLY: True, but there are two ways that elements can be related. One is that they have similar chemical properties. And that, Mendeleev did know about. To make the periodic table with only these experimental and empirical facts is an amazing achievement. The second way elements can be related is to have similar atomic structures, in terms of the way their electrons are arranged. And in fact they have similar chemical properties because their electron arrangements are similar.
SIGRID: OK. Now, in this periodic table, where it describes lithium as , I get that \(_{3}^{7}\textrm{Li}\) is a shortcut for lithium…
SALLY: …That’s right, but they aren’t always sensible like ‘\(\textrm{Li}\)’. For example, ‘\(\textrm{Au}\)’ is gold.
SIGRID: Oh, OK. Well I suppose I’ll just have to learn those then. So does lithium have 3 protons and 7 neutrons?
SALLY: No. You might think that. And the 3 is indeed the number of protons. But the 7 means the total of the protons and neutrons in the nucleus.
SIGRID: Which means the total is 7, and 3 of them are protons. So there must be 4 neutrons.
SALLY: Exactly.
SIGRID: But that’s more conceptually complicated than just labelling it with the number of neutrons.
SALLY: More conceptually complicated maybe, but more useful. Have another look at your table of protons, neutrons and electrons, and tell me what the protons and neutrons have in common.
SIGRID: Oh, they both have one unit of mass, and together they pretty much account for the mass of atoms.
SALLY: And because normal stuff is made of atoms, they account for the mass of normal stuff. So if carbon is \(_{6}^{12}\textrm{C}\) and oxygen is \(_{8}^{16}\textrm{O}\), that means that an oxygen atom has 16 units of mass and a carbon atom has 12 units of mass. That number is called the mass number.
So does that mean that if you weigh oxygen and carbon out in the ratio of masses 16:12, the two lumps will have the same number of atoms?
SALLY: Yes! 16 g of oxygen has the same number of atoms as 12 g of carbon. 32 g of oxygen has twice as many atoms as 12 g of carbon. And that’s useful to know if you are trying to burn carbon to make carbon dioxide, because every carbon atom needs 2 oxygen atoms, just like in your drawing earlier.
SIGRID: That means if you have 12 g of carbon, you would need 32 g of oxygen, so that neither element has any left over.
SALLY: Exactly.
SIGRID: And you can just scale it up or down. Because you probably don’t have 12 g of carbon. If you had 3 g of carbon, that’s one quarter the amount, so you would need 8 g of oxygen because it’s one quarter of 32.
SALLY: Your career as a synthetic chemist awaits! So you see why it’s more useful to display the top number as the mass number, rather than the number of neutrons.
SIGRID: Yeah, it helps you weigh out the right amount of stuff. And we can always find the number of neutrons if we need to from the difference between the two numbers. So in a \(_{9}^{19}\textrm{F}\) atom, there are 9 protons, 9 electrons and 19 – 9 = 10 neutrons. So what’s going on here? My periodic table gives \(_{17}^{35.5}\textrm{Cl}\), but you can’t have 18 and a half neutrons. Can you?
SALLY: No, but actually that’s the least of your worries. Look at this portion of a more sophisticated periodic table. None of the mass numbers are whole numbers!
SIGRID: Go on then. What’s happening?
SALLY: Well, have a look at these pictures of six atoms, and tell me what you see.
SIGRID: OK. Five of them are lithium because they have three protons. And the bottom-right one is beryllium, because it has four protons.
SALLY: Good. Anything else?
SIGRID: One of the lithium atoms is different from the others because it has an extra neutron.
SALLY: Exactly – the one at bottom-centre. Forms of the same element with different numbers of neutrons are called isotopes. They do the same chemistry, because there is basically no difference in what their electrons are doing, but they vary in mass.
SIGRID: And in a ‘lump’ of an element there will be trillions of atoms and you might have more than one form, so that the top number is like an average of the mass numbers of all the atoms in the lump.
SALLY: Exactly. So the mass number describes a specific isotope, for example the ‘4’ for helium in your simpler periodic table. Whereas the ‘4.00260’ in my more sophisticated table describes the mixture of isotopes that actually exists, and is called the relative atomic mass.
SIGRID: Why didn’t my easier periodic table do that?
SALLY: I suppose it was probably trying to simplify things for you. It just picked the most common isotope, worked with that and ignored the others. I admit the chlorine thing is a bit confusing because they have used two isotopes for that, but I guess chlorine’s average is further from a whole number than most of the others, so they felt they had to.
SIGRID: In that case, does chlorine have an equal mixture of two isotopes with mass numbers 35 and 36?
SALLY: Well, that would work, but in fact the isotopes in question have mass numbers 35 and 37.
SIGRID: That means there must be more of the 35 than the 37, to make the average 35.5, which is closer to 35 than to 37.
SALLY: Exactly.
SIGRID: And going back to our new, improved periodic table, rather than saying that 32 g of oxygen reacts with 12 g of carbon, we can now say that 15.9994 g x 2 = 31.9988 g of oxygen reacts with 12.0111 g of carbon.
SALLY: Yes!
SIGRID: But what’s happening with hydrogen? If it is \(_{1}^{1}\textrm{H}\), then it has 1 proton and no neutrons.
SALLY: That’s right. It’s the simplest atom – just one proton with one electron ‘orbiting’. In the history of atomic theory the hydrogen atom was really important, because it’s often nice to try to solve the simplest example first, and then make adjustments for the harder cases. So in 1913 Niels’ Bohr came up with a theory of the hydrogen atom.
SIGRID: Why did he bother? I mean, don’t we already have a theory – one proton with one electron orbiting it?
SALLY: There was a theoretical problem and a conceptual one. The theoretical problem is that an orbiting electron must be accelerating (because all things moving in circles are changing their direction, hence changing their velocity, hence accelerating). And accelerating charges radiate electromagnetic energy. So electrons should, by right, radiate away their energy and spiral down the plughole of the nucleus, if you like, never to be seen again. Bohr suggested that electrons could only exist in discrete orbits, each at a particular distance from the nucleus. The greater the radius of the orbit, the higher the energy of the electron.
SIGRID: Oh, so that’s why I see pictures of atoms like this.
SALLY: Yes. To move an electron to a higher orbit requires an input of energy, maybe from absorbing a photon of light, or maybe from a collision with another atom.
SIGRID: What’s a photon?
SALLY: Light exists in little particle-like packets of energy called photons. The energy of a photon is related to the wavelength of the light. When you read a book, there are countless photons travelling to your eyes (and everywhere else – the direction of your eyes isn’t special), and your brain interprets the signal from all those discrete packets of energy as a coherent, continuous picture of the words on the page.
SIGRID: A bit like when you pour sand you get the impression of a single fluid rather than a collection of grains.
SALLY: Yes – quite like that.
SIGRID: What happens to the energy when the atom has absorbed it? Does it stay in the atom somehow?
SALLY: Generally, no. And what I’m about to say is one of the most important lessons of this whole tale… Have you ever heard of Sisyphus?
SIGRID: Yeah, Greek guy. What, he’s the most important thing?
SALLY: No! He’s an analogy for the important thing. I wish I hadn’t mentioned him now. Anyway, too late – why is he famous?
SIGRID: Well, unless he’s the guy who kept getting his liver eaten…
SALLY: He’s not.
SIGRID: …then he was condemned to push a boulder up a hill forever, and it kept falling back down again. What has this got to do with…? Oh, I see. Boulders spontaneously fall downhill, not uphill. To get a boulder to move uphill you need to put in some energy.
SALLY: And therein lies the message. Spontaneous processes tend to occur so as to move to a state of lower energy. The boulder has less potential energy at the bottom than at the top. The electron has less energy in the inner orbit than the outer orbit.
SIGRID: And so the electron spontaneously falls back down into the inner orbit. What happens to the energy?
SALLY: Well, how did we ‘excite’ the atom? In other words, how did we move the electron ‘uphill’ to a higher energy level?
SIGRID: We got the atom to absorb light. Oh, I see, so in reverse, when the electron falls back to a lower energy level, it releases that energy in the form of light.
SALLY: Yes. As a photon with a fixed amount (a ‘quantum’) of energy equal to the difference in energies between the two orbits. That’s your first meeting with the word ‘quantum’!
SIGRID: So a hydrogen atom spends its life with the electron in the lowest orbit, unless something makes it jump up, at which point it will jump back down and release a photon of light.
SALLY: We’re going to start calling the orbits ‘energy levels’ now, because the energy of them is the most relevant thing at this stage. We can draw the energy levels of the hydrogen atom as a one-axis graph, like this.
The lowest energy state for the atom is called the ground state (like the ground floor of a building); the others are called excited states. The units on the axis are electronvolts. Don’t worry about them – they are just a unit of energy that is conveniently small for processes on this scale.
SIGRID: What’s n?
To be continued… Find Part 3 here.
And have you worked out yet why the characters are so named…