Half-life part 2 Introduction This lesson follows on from lesson 3 so it might be worthwhile quickly revising that before you start. Radioactivity is measured in becquerels. The unit of radioactivity is named after Henri Becquerel, who discovered it. A given isotope always takes the same amount of time for the count rate to decrease by a half.
For example, it might take 10 years for the count rate to drop from 80 Bq to 40 Bq; another 10 years to drop from 40 B to 20 Bq; another 10 years to drop from 20 Bq to 10 Bq and so on. In this case the half-life is 10 years. Different samples of the same isotope all have the same half-life The half-life of a particular isotope is always the same. If we had a bigger sample of the same isotope then the count would be higher, say becquerels.
Using half-life in simple calculations What would its radioactivity be after 30 years? Each half-life is 10 years. So we imagine going in forward one half-life at a time from ZERO years: Then we halve the count for each half-life: We can use the same idea to find out how long it would take for a sample with radioactivity Bq to drop to 30 Bq.
Carbon dating can only be used to find the age of things that were once alive, like wood, leather, paper and bones. If you have a wooden box, carbon dating can tell you when the tree to make it was cut down but not when the box was made.
Carbon dating can be used to date things up to about 60 years old. So how does it work? Trees are made from reorganised air Many people think that plants grow by taking food from the soil through their roots but this is not true. All green plants make their own food in their leaves. They make it from carbon dioxide in the air. This process is called photosynthesis. You need energy from the Sun and lots of water.
Carbon dioxide is made into simple sugars and it is these that are the building blocks that make up wood, bark and leaves. Animals eat plants or other animals that eat plants so animals are also mostly rearranged carbon dioxide.
Carbon is produced in the upper atmosphere by cosmic rays. It is a beta emitter with a half-life of about years. Carbon is constantly created and constantly decays Carbon is produced all the time but it also decays all the time back into nitrogen An equilibrium is reached whereby about one in a trillion carbon atoms in the atmosphere is carbon Carbon in living things decays all the time but is replaced by carbon in food.
All new cells are made from food. All food ultimately comes from green plants making sugars from carbon dioxide. So all living things contain exactly the same proportion of carbon compared to carbon This is assumed to have stayed fairly constant. A living adult human body contains about a billionth of a gram of carbon This means a human adult has a radioactivity of around becquerels due to carbon This is actually very small. When a living thing dies they stop eating so no new carbon When a living thing dies the cells are no longer replaced so no new carbon enters it.
The radioactivity of the carbon begins to decrease. It halves about every years. By measuring the radioactivity we can tell how long ago the living thing died. Remember that the carbon decays all the time whether the thing's alive or not. It's just that when it's living the carbon is constantly replaced so the overall radioactivity stays constant. Preparing a sample for carbon dating Say we want to find the age of an old dead tree. Animals and plants have similar amounts of radioactive isotopes, particularly potassium, another beta emitter.
A common way to isolate the carbon is to carefully burn a piece of the wood and use the carbon dioxide given off. The carbon dioxide is separated out from the other gases. It is mostly carbon with tiny amounts of the radioactive carbon Calculating the age by comparing the count with the atmosphere We measure the radioactivity of the carbon dioxide in a special chamber to shield it from background radiation.
We can then compare it with the radioactivity of the same amount of carbon dioxide from the atmosphere. The oldest samples have the lowest radioactivity. The radioactivity halves with each half-life. This means we can calculate the age of a sample. Even this kind of carbon dating can only be used to date things that were once alive and died less than about 60 years ago.
Other radio-dating techniques are used to date ancient rocks. Displaying radioactive decay on a graph We can plot a graph of radioactivity against time for our sample that had a half-life of 10 years. You can move forward in time and watch where on the graph you are. We can use our graph to show that it always takes 10 years for the radioactivity to drop by a half regardless of where you are on the graph.
The decay of protactinium experiment A common school experiment is to find the half-life of an isotope called protactiniumm. Take results, plot a graph and then calculate the half-life. There's nothing special about half-life It's not that radioactive isotopes 'have' a half-life.
They get less radioactive in a way that's called an exponential. Exponential decay means that equal periods of time give equal proportional changes in radioactivity. So you can pick any period of time, say 1 minute, and measure how much the radioactivity drops to in that minute. We could equally well choose the one-third life or the four-fifths life.
Why radioactivity decreases with time: When a nucleus decays two things happen The nucleus changes to become more stable Some nuclear radiation is given off, e. Remember the nucleus is just part of an atom, except that, when we talk about radioactivity, we tend to ignore the electrons that take up most of the volume. The atoms can't just vanish into nothingness and neither can its nucleus.
The nucleus simply changes. Let's think about a sample of a beta emitter. The sample consists of billions of atoms. The nucleus of each atom is unstable.
Each nucleus will emit a single beta particle and then become stable. So every time a nucleus changes it gives out a beta particle. One nucleus, one particle. But as time passes there are fewer undecayed nuclei left TO decay. You can say this about the undecayed nuclei: So the fewer undecayed nuclei you have, the slower you lose them, and the lower the radioactivity. There are lots of curves that look like exponentials but they don't have constant half-lives.
Half-life is constant because every nucleus has a constant chance of decay each second. But the decay of a given nucleus is completely random. Nuclei never grow old The next point is slightly more subtle. A ninety year-old person is more likely to die this year than a sixteen year-old. Step forward in time and see that you can't predict when the nucleus will decay.
At the start of every second it has exactly the same chance of decay. But if we have no idea at all exactly when a particular nucleus will decay how can we know how the radioactivity of a sample of trillions of nuclei will change with time?
You know how many nuclei will decay, you just don't know which ones Imagine a large number of nuclei. And this chance never changes. High chance of decay means short half-life But different isotopes have different chances of decay. In other words different isotopes have different half-lives. If you measured half-life with enough precision you could say that every half-life is unique. If you have three nuclei, each from different isotopes, then one will have the highest chance of decay and one will have the lowest.
But you have no idea which one will decay first. It only makes sense to talk about likelihood when you have lots of nuclei for each isotope. You still can't predict which one will decay first, only the probability. Radioactivity is proportional to the number of undecayed nuclei Imagine you have a sample of millions of nuclei of a beta emitter.
Over time the undecayed nuclei decay. The rate of beta emission i. In fact the radioactivity is directly proportional to the number of undecayed nuclei.