Toppling wooden blocks to model nuclear decay intuitively

What does a nucleus get out of the process of decay? Why does it bother?

The answer is that the nucleus becomes more stable. Systems become more stable when they go from a high energy arrangement to a lower energy one. This means the system releases energy.

For example a domino on its end is unstable. Give it a little push and it ends up flat on the table. The centre of gravity has got lower and so the energy of the system has decreased. This energy appears as vibrations of the air (i.e. sound), of the table and of the domino. The vibrations rapidly become smaller-scale and less ordered, ending up as internal energy of the atoms. So the temperature rises a little.

You can model a nucleus as two upright wooden blocks standing on top of each other. This little tower is quite unstable. Give it a little push and it falls over. There are three ways of making the tower more stable that are analogous to alpha, beta and gamma decay.

For alpha decay, simply remove the top block. Making a big nucleus a little smaller increases its stability.

For beta decay, replace the top upright block with a shorter one. Changing a nucleon from a neutron into a proton can make a nucleus more stable.

For gamma decay, place the top block on its side so the blocks stay the same but the configuration is different. Letting nucleons settle down into a lower energy pattern makes the nucleus more stable.

Here is an interactive animation modelling alpha, beta and gamma decay with wooden blocks.

Are high resistance bulbs brighter?

Energy is dissipated quicker in high resistance bulbs because the current has to try harder to get through - so they’re brighter, right?

Wrong - though it can be a seductive argument. One of the problems is the deeply ingrained idea that current flow is sequential. The incorrect story is that the electrons move happily through the low resistance wires but when they come to the bulb filament they find it difficult to squeeze through and all the jostling transfers energy to the filament, which we experience as heat and light. The higher the resistance, the more jostling and the brighter the bulb.

This is also an example of what you might call ’local reasoning’. With circuits you have to think about what happens to every element in the circuit all at the same time: it normally causes problems if you focus in on one part and then another.

In fact what happens is that a higher resistance bulb decreases the current everywhere in the circuit. The slower moving charges transfer energy to the bulb at a lower rate and so the bulb is dimmer.

One other subtlety is that in a circuit energy is transferred quickest in the places where the resistance is RELATIVELY high. But the higher the actual (rather than the relative) resistance, the slower the overall energy transfer and the dimmer the bulb.

You can check out an animation explaining what happens when a very low resistance bulb is connected first to 12V made from joining small cells in series and then connected to 12V from a car battery.

Decay never means disappear: problems with the dice analogy

It’s common in schools to model radioactive decay using a large number of dice. All the dice are thrown at once and the sixes are removed and put to one side. The process is repeated lots of times until all the dice have ’decayed’. This gives a nice feeling for exponential change since the fewer dice there are left the fewer sixes are thrown.

The problem with this analogy is with the removal of the dice. If you're not very careful it gives the impression that when a nucleus decays it disappears. This misconception even leaks into computer simulations. For example this very misleading simulation is in the top two Google results if you search for ’radioactive decay simulation’.

Nuclear decay happens when an unstable nucleus changes into a more stable form by emitting a particle. It never means the nucleus disappears. For example with alpha decay the nucleus gets smaller, with beta decay a neutron changes into a proton and with gamma decay the nucleus settles into a more stable ’shape’.

I've never come across a simulation (apart from with our Furry Elephant simulation of radioactive decay) where the emitted alpha or betas are actually shown. This is after all what you observe with your Geiger counter and there is a one-to-one relationship. Each decay gives rise to one particle.

Why do thick wires have lower resistance?

Even the most apparently reputable sources of information are sometimes full of misconceptions. The BBC manages to demonstrate several all at the same time with this terrible animation trying to explain why thicker wires have a lower resistance than thin ones.

The main argument is that a thick wire has ’more space’ for the electrons to move around in than a thin wire. But wires are made from atoms - that's where the free electrons come from. So thicker wires have more atoms and so no more empty space (per cross-sectional area) than thin ones. Another implication of the animation is that the wires are like empty tubes. This suggests that the electrons come from the battery as a sort of source rather than already being there everywhere in the circuit. The final problem is the speed of the electrons. Since the animation shows a longer path for the electrons in the empty thick wire their speed must have increased. In fact, the opposite is the case. Electrons travel slower in thick wires.

For a copper wire (at a given temperature) the speed of the electrons depends only on the voltage across it. Imagine a three-lane road and a single-lane road with cars all going at the same speed. More cars pass per second in the wider road even though the speed is the same. More cars (charges) per second means higher current for a given voltage and so smaller resistance.

Here's an animation showing how thicker wires have a lower resistance.

Since current is the same around a simple series circuit the charges have to go faster where the wire is thinner. Faster charges mean more interactions with the ionic lattice per second and so higher resistance.

Is Alpha Radiation Really More Ionizing than Beta?

When an alpha particle speeds through air it rips electrons off the molecules that it passes close to. The electrons don't just attach themselves to the alpha particle and neutralize it. They're flung a long way away from their parent atom and the air ion that's left tends to stick around for some time afterwards.

Every time it ionizes an air molecule the alpha particle loses a little energy to the emitted electron and slows down. After a few thousand ionizations it has almost stopped and the alpha grabs a couple of electrons from nearby molecules and ends up as a neutral helium atom. Perhaps counter-intuitively the alpha makes more ionizations per distance when it's going slowly than when it's going fast. If you imagine that the electron has to reach a certain speed before it is ejected from the atom then the faster the alpha moves the less time there is to reach this speed before the alpha is out of electrostatic range.

Beta particles have a much smaller mass than alpha particles. This means a beta with the same kinetic energy as an alpha will be moving much faster. Because it's moving faster and also has only half the electric charge it is less likely to ionize an air molecule as it whizzes by. For this reason the ionizations from a beta particle are much more spread out than for an alpha. An alpha and beta of the same energy will make similar numbers of ionizations before stopping. But the alpha particle will make them in a shorter distance. This is what we really mean when we say alpha radiation is more ionizing than beta.

The Speed of Electrons in Wires

When you flick a light switch the light comes on straightaway. A common misconception is that this is because the electrons leave the power supply and travel very quickly through empty wires and then back to the power supply again.

In fact the electrons are already there everywhere in the circuit and they all start moving very slowly at almost exactly the same time. Just like a wheel, there's no part that begins first.

If you look a little more deeply there are actually three very different speeds, which are very difficult to imagine all at the same time.

1. (VERY FAST) The random thermal jiggling of the electrons. The electrons whizz around colliding billions of times a second with the surrounding atoms (or, more accurately, ions). This depends on the metal and the temperature but is typically around 1% of the speed of light.

2. (VERY VERY FAST) The speed at which the electrons find out that they should start moving. Think of the rear carriage of a train starting to move at almost exactly the same time that the locomotive begins to pull. This is called the signal speed and is typically a bit less than the speed of light.

3. (VERY VERY SLOW) The speed that the electrons actually make progress along the wire. This is called the drift speed and is typically around half a metre an hour - slower than a snail. This is because the electric field in the wire (think push from the battery) doesn't have much space to accelerate the electrons before their high thermal speed causes them to be scattered off another atom.

In this simulation I try to show all three speeds at the same time.

Half-life and Health Risks

Imagine radioactive material is accidentally released into the environment. Which is the most hazardous half-life for it to have? A few hours? A few years? Millions of years?

To answer this question we need to think about why radioactivity decreases with time. The simple answer is that every time a nucleus decays and releases a particle (like an alpha or beta) then there's one fewer undecayed nucleus left. For a given isotope every nucleus has the same chance of decay each second. It doesn't matter how long it's already been around for or what its neighbours are doing.

If the chance of decay is high then lots of nuclei decay each second (so lots of radiation is given off) but you quickly end up running out of undecayed nuclei. This means the half-life is short.

If the chance of decay is low then very few nuclei decay each second (so very little radiation is given off) and there are still lots of undecayed nuclei left a long time later. This means the half-life is long.

The key point is that isotopes with a very long half-life are only very weakly radioactive and isotopes that are very radioactive don't stay radioactive for long.

It turns out that the most problematic half-life for the environment is a few decades or so. Isotopes such as strontium-90 (with a half-life of about 30 years) are pretty radioactive and stick around for a time comparable to a human life-time, which gives plenty of opportunity for them to cause genetic damage.

In this activity you go forward in time to see the effect on radioactivity of different samples.

General comments about Radioactivity and Atomic Physics Explained

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The Constant Current Misconception

If you have a simple battery and bulb circuit and you add another bulb in parallel, would you say the current now 'splits' at the junction?

Or imagine starting with the same simple circuit and adding a bulb in series. Could you explain the fact that the bulbs are both dimmer by saying that the battery’s energy is now shared between two bulbs?


If you think either of these explanations seem pretty reasonable then you may hold the constant current misconception.

The constant current misconception is the implicit belief that batteries are constant current providers.

In the parallel example there isn't a 'the current' to split. When you add the extra bulb in parallel then the current drawn from the battery doubles, it doesn't just split differently.

In the series example the assumption is extended to imply that batteries provide energy at a constant rate. They don't. When the extra bulb is added in series then the battery provides energy at half the rate. It doesn't provide energy at the same rate and then share it out differently.

Batteries are constant voltage providers (as long as you don't make them work too hard) and the current they provide depends on the circuit they are connected in. Any change to the circuit will always change the current.

General comments about Electricity Explained

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An Introduction to the Philosophy of Science

Imre Lakatos once said that most scientists have no more idea of the nature of science than a fish has of hydrodynamics. A little harsh, perhaps, but I'm inclined to be deeply cynical of those who blithely talk about science as if there existed this human acitivity that churned out universal truths simply by following a recipe.

I've tried to summarise some of the main ideas in the philosophy of science and I have to say I'm becoming more of a fan of Paul Feyerabend (having just finished re-reading Against Method for the third time) as I get older.

Teaching How Science Works

The emphasis on embedding How Science Works into syllabuses is welcome but my guess is that many teachers, even those who have been research scientists, can find it hard to deliver.

This isn't just because it's difficult to find interesting activities to get across the idea of, say, peer review but more because science is often taught as an end-result rather than a process. And here I'm not talking about 'investigations'. I'm talking about impetus theory and flogiston.

I've taken a fairly uncontentious approach to introducing How Science Works but I'm still deeply suspicious of the idea that there exists some 'scientific method' that leads to 'the truth'.