# Radioactive Half-life

## Radioactive Half-life Revision

**Radioactive Half-life**

Because radioactive decay is **random**, you cannot predict when a single nucleus will decay. However, you can predict how long it will take for **half of the nuclei** in a sample to decay. This is called the **half-life** of the sample.

**Calculating Half-life**

The definition of half-life is the time taken for the **count rate** from a sample to decrease to **half the initial value**. If we use a radiation detector, such as a **Geiger-Muller tube**, we can measure the radiation being emitted from a a sample and calculate the radioactive half life from the results.

First, you need to plot a** graph** of the **counts per minute** against the** time**. Then, extrapolate the time taken for the counts to reduce by a half. In this example, the original counts was measured to be 300 \text{ counts per minute} and so half the counts is 150 \text{ counts per minute}. You can see from the graph that this corresponds to 9 \text{ days}. Therefore the half-life of this sample is 9\text{ days}.

**Calculations Using Half-Life**

If we know the half-life of a sample we can determine how much smaller the count rate will be after a given number of half-lives.

For example, after 2\text{ half-lives}, the radioactivity of a sample will be \dfrac{1}{2}\times \dfrac{1}{2} = \bold{\color{f21cc2}{\dfrac{1}{4}}} **of the original radioactivity**. This is the same as saying it is 4 times smaller.

After 3\text{ half-lives}, the radioactivity will be \dfrac{1}{2} \times \dfrac{1}{2} \times \dfrac{1}{2} = \bold{\color{f21cc2}{\dfrac{1}{8}}} **of the original activity**, or 8 times smaller.

## Radioactive Half-life Example Questions

**Question 1:** What is the definition of radioactive half-life?

**[2 marks]**

The time taken for the **radioactivity** of a sample to **reduce by half**.

**Question 2:** Explain what is meant by the statement “radioactive decay is a random process”.

**[1 mark]**

You cannot predict **when an individual nucleus will decay**.

**Question 3:** A student measures the count rate from an unknown sample and plots their results against time on the following graph. Calculate the half-life of the sample.

**[2 marks]**

Half of the original counts per minute is \dfrac{140}{2}=\bold{70}

(Using graph) half-life is therefore \bold{1.4}\text{ minutes} (or any value between 1\text{ minutes} and 1.5 \text{ minutes}).

**Question 4:** A radioactive substance with a half life of 1 \text{ hour} has an activity of 100\text{ Bq}. What is the activity of the substance after 4 \text{ hours}?

**[2 marks]**

4 \text{ hours} = \bold{4\text{ half-lives}}** **