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Half-life – WJECModelling radioactive decay

Radioactive isotopes are used for blood flow monitoring, cancer treatment, paper mills, carbon dating and smoke alarms. Each isotope used in these applications has a characteristic half-life.

Part of Physics (Single Science)Forces, space and radioactivity

Modelling radioactive decay

When a radioactive nucleus decays, it does so randomly. You can’t predict when it will happen. Lots of nuclei of the same isotope, however, will decay following a pattern called a radioactive decay curve.

The decay of radioactivity in a radioactive element can be modelled using cubes, dice or coins.

In decay, a radioactive parent randomly emits an alpha or beta particle and turns into a new daughter element. The daughter element is more stable. For this example, we will use coins.

Step one. Collect the coins and count them. This is the starting number of parent radioactive atoms. Record this number. Between 60 and 100 coins is a good starting number.

Step two. Put the coins into a container, shake them, and then throw them into a tray.

Step three. Remove coins showing heads. These represent atoms that have decayed.

Step four. Count the remaining coins and record the number in a table against the throw number.

Step five. Repeat steps two to four until only two or three coins remain.

Step six. Plot a graph of number of coins remaining (\(\text{y}\)-axis) against throw number (\(\text{x}\)-axis).

Stacks of silver coins

The remaining coins will form a pattern like the coins in the picture.

This animation explains more about plotting a radioactive decay curve graph.

Plotting a graph of the remaining coins against the throws will produce a curve similar to this.

Graph titled Coins against throws for a decay simulation. The Total coins on the y-axis goes from 0 to 450. Throws on the x-axis goes from 0 to 10.

Use the graph to answer the question.

Question

What was the starting number of coins?