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Hello, my name's Dr.

George, and this lesson is all about radioactive half-life as part of the unit nuclear physics.

The outcome of the lesson is I can describe the random nature of radioactive decay and the predictability of radioactive half-life.

Here are the key words for this lesson.

I'll introduce 'em as we go along, but you can come back to this slide any time if you need a reminder of the meanings.

The lesson has two parts: random nuclear decay and half-life patterns.

Let's start with random nuclear decay.

The outcome of a random event isn't influenced by anything.

It's completely down to chance.

And an example is a fair coin toss, which has a 1 in 2, 50%, chance of resulting in heads and the same chance of resulting in tails.

A fair roll of a die has a 1 in 6 chance of resulting in any particular number.

Here's a question for you.

Aisha rolls three fair dice of different colours.

Which one is most likely to land on a 1? When I ask a question, I'll wait five seconds, but press pause if you need longer, and press play when you have your answer ready.

And the answer, the odds are the same from each die.

So the probability of any particular number being rolled has nothing to do with the colour.

Only the number of sides affects the probability.

Now, Izzy rolls a fair die which has 8 sides.

What is the likelihood of her rolling the number 5? The correct answer is exactly 1 in 8.

Each of the 8 numbers has an equal chance of being rolled.

So the odds of rolling a number 5 are 1 out of 8 possibilities.

1/8.

The outcome of a random event isn't influenced by the events that happened before it.

So each toss in a series of coin tosses has a 1 in 2 or 50% chance of resulting in heads no matter what the previous pattern has been.

Here's an example.

You can't know from this that it's going to go tails, heads, tails, heads.

And you can't know from this whether it's going to be heads again or change back to tails.

Each time the odds only depend on the fact that the coin has two sides.

Alex tosses a fair coin five times with the results shown on the right.

What is the likelihood of him throwing tails next throw? And again, it's exactly 1 in 2.

The coin has no memory of what's come before.

It's not going to try to come up heads because there has been a run of tails.

Radioactive decay is a random process.

The decay of an unstable nucleus isn't influenced by outside factors such as the pressure or the temperature or a chemical reaction taking place.

So it's not possible to predict whether an individual nucleus will change through radioactive decay during any particular period of time.

Which one is not random? The correct answer is B.

Whether a goal is scored from a penalty kick doesn't purely depend on chance.

It depends on various factors including the skill of the person taking the penalty and of the goalkeeper.

But random behaviour isn't always unpredictable.

If there are a large number of random events each with identical odds, then an outcome can be predicted overall.

For example, tossing sets of 100 identical coins four times gave the results shown in this table.

Each time you can't say that you'll certainly get exactly the same number of heads and tails, but if you do this enough times, it will work out to be exactly or nearly exactly 50/50.

Now, a set of 32 coins are flipped several times and all of those showing heads are removed each turn.

If this is done, each turn close to half of the remaining coins land heads up and are removed.

After 0 turns, of course, there's still 32 coins remaining.

Then we flip them all once and let's say 15 coins remain, we take the ones that remained, flip them again, 8 remain and then 5 remain.

It's not exact, but there's a definite pattern in this random behaviour.

Each time close to 50% of these coins are landing on heads, and this behaviour shows that random behaviour can be modelled if a large enough number of identical objects are used.

Here's a graph for the same experiment with 80 coins.

When the chance of landing on heads is always 1 in 2, the number of survivors will halve on average every time a set of coins is tasked.

A large number of dice can be used to model the pattern of decay of unstable nuclei.

Each die represents a nucleus and it has an identical chance of landing on 1 each time it's rolled.

All of the dice are rolled and any landing on one as said to decay and the decay dice are removed and the surviving dice are rolled again.

So these represent the nuclei that haven't yet decayed.

Each roll models a one second period of time.

Over time, over a series of rolls, the number of dice surviving will decrease in a predictable pattern just like identical unstable nuclei decay following a predictable pattern.

Now, you are going to try this investigation.

You'll need 100 dice, count them into a tray, and then you'll roll them all into the tray.

Take care not to lose any over the sides.

And then remove all dice, which show a 1.

Record the number of dice remaining and the number removed.

You'll need to create a table for this.

And then repeat steps two to four with the remaining dice until you've completed 10 rolls.

Finally plot a graph of the dice remaining on the y-axis against the roll number on the x-axis.

So press pause when you do this, and press play when you've finished.

I hope that went well.

Here's a set of example results.

Yours will be similar, but they're very unlikely to be exactly the same.

Although each die is behaving randomly altogether, the dice behave in a reasonably predictable way.

Now, I described this earlier as a large number of dice 100, but didn't say a test tube sized sample of a radioactive isotope, there'll be something like a trillion, trillion nuclei.

And when you're dealing with those numbers the decay curve will be very smooth and predictable indeed.

Now, let's look in more detail at half-life patterns.

When a large number of identical dice are rolled, the fraction that end up showing one will only depend on the number of sides the dice have.

If you use six-sided dice, about 1/6 of the dice will show a 1 if you roll them all.

If you use eight-sided dice, about 1/8 of them will show a 1.

Over a series of rolls where decayed dice are removed, a decay pattern forms. And the pattern formed is called a decay curve.

And hopefully your graft looks rather like one of these.

The shape of the curve depends on the number of sides the dice have because it depends on the chances of decay the odds of decay on each roll.

The more sides the dice have, the slower the decay, the longer it takes for more of them to decay.

This graph is for six-sided dice and this one is for eight-sided dice.

Three sets of dice each with different numbers of sides are tested.

Which set has the most sides? The answer is set C.

Having more sides means the chance of decay is lower, so the number remaining falls more slowly.

And radioactive nuclei behave in a similar way to dice.

They decay with the same shape of decay curve.

This one is an example.

And the probability of decay within each unit of time depends on what type of isotope this is.

The length of time it takes for half of the nuclei in a sample of radioactive isotope to decay is known as its half-life.

If an isotope has a half-life of four minutes, that means that after four minutes, there'll be half of the original nuclei remaining, the other half will have decayed into some other type of nucleus.

If you look at the graph, you can see that we started with 100% of the nuclei on decayed, and then after four minutes, that's dropped to 50%.

After eight minutes, the percentage remaining has fallen to 25%, so it's halved again.

And if you halve and halve again, you have a quarter of the original nuclei remaining.

After 12 minutes, three half-lives, the original number has halved and halved again and halved again.

We have an eighth of the original nuclei still under decay.

All atoms of the same isotope are identical, and so samples of a particular isotope will all have the same half-life.

But different types of isotope have different half-lives to each other, and these vary enormously.

In this table, we have half-lives as short as one millisecond, so in a pure sample of thorium-217, half of the nuclei will decay in just a millisecond and there are half-lives even shorter than that, nanoseconds or shorter.

But half-lives can be very long.

Uranium-238 has a half-life of 4.

5 billion years, which is similar to the age of the universe.

Which of the isotopes shown on the graph has the shortest half-life? And the correct answer is isotope B.

We could realise that from the fact that its graph falls fastest over time or we could look at the numbers.

We can see that for isotope B, there's 50% of the original nuclei remaining after two minutes, whereas for isotope A, that takes three minutes.

And for isotope C, it takes four minutes.

The half-life of isotope B is two minutes and it's the shortest.

Now, a longer challenge for you.

Some students are using a pizza to explain radioactive half-life.

They cut the pizza in half and eat 1/2, then they cut the remaining piece in half and eat half of that.

And they repeat this several more times.

So this is a kind of model for trying to understand radioactive half-life.

Three questions for you.

Can you state three ways in which this is an accurate model for explaining half-life? State three ways in which this is not an accurate model.

And describe how the model could be improved to explain half-life better.

Press pause while you write down your answers.

And when you press play, I'll show you some example answers.

Here are some ways in which this is a good model for explaining half-life.

The remaining portion of pizza is the same proportion of pizza as a proportion of radioactive nuclei that have not undergone radioactive decay.

So after the first round, it's half, then it's a quarter, and so on.

The portion of the pizza that's eaten represents the proportion of radioactive nuclei that have undergone radioactive decay.

The pizza that's been eaten hasn't disappeared.

It's just changed.

It's changed into chewed up food.

And the nuclei that decay don't disappear.

Their atoms simply change into atoms of a different isotope.

And if a time taken for students to cut and eat the pizza each time is always the same, then each repeat represents one half-life.

Ways in which this is not an accurate model.

Here are some of the things you could have said.

When radioactive atoms decay, the atoms they decay into have usually not moved out of the radioactive material, whereas the eaten pizza is no longer on the plate.

The size and mass of the radioactive material remains almost exactly the same during the time the radioactive atoms are decaying because they decay into atoms that have similar mass as the original ones.

Radioactive atoms decay randomly throughout a radioactive material during a half-life rather than half of them all eaten at the same time.

And the time it takes for each half to be eaten and to decay is likely to get less and less as more of the pizza is eaten.

The pieces that get eaten in later rounds are smaller and smaller.

And finally, each portion that's eaten could be replaced by an equal size portion of a different type of pizza.

This would represent how the unstable atoms are replaced by different, more stable atoms, at least for alpha or beta decay.

Rather than half of the whole pizza being replaced, half of each quarter perhaps could be replaced and so on, representing how radioactive atoms decay throughout the whole material, throughout the whole pizza rather than all on one side.

A timer could be used to time each cutting and halving of the radioactive atoms in the pizza so that each half-life is always the same length of time.

And different pizzas could be used, each one with a different length of half-life to represent different decaying isotopes.

Well done if you've got some of these ideas into your answers, and you might have thought of some other good ones too.

And now, we've reached the end of the lesson.

So here's a summary.

The result of a random event is entirely due to chance.

Nuclear decays are random processes.

The radioactive decay of a specific unstable nucleus cannot be predicted or influenced.

The pattern of decay can be predicted when there are large numbers of identical probabilities over time.

Nuclei decay in a pattern known as a decay curve like the one shown here.

And radioactive half-life is a time taken for half of the nuclei of a radioactive isotope to decay.

Well done for working through this lesson.

I hope you found it interesting.

And I hope to see you again in a future lesson.

Bye for now.