Half-Life (AQA GCSE Combined Science: Synergy: Life & Environmental Sciences): Revision Note

Random Nature of Decay

• It cannot be predicted when a particular unstable nucleus will decay

• This is because radioactive decay is a random process, this means that:

  • There is an equal probability of any nucleus decaying

  • It cannot be known which particular nucleus will decay next

  • It cannot be known at what time a particular nucleus will decay

  • The rate of decay is unaffected by the surrounding conditions

  • It is only possible to estimate the probability of a nuclei decaying in a given time period

• For example, a researcher might take some readings of background radiation

• If the researcher reset the counter to zero, waited one minute and then took the count

  reading and repeated the procedure, they might obtain results such as:

32    11    25    16    28

• The readings don't appear to follow a particular trend

  • This happens because of the randomness of radioactive decay

Dice Analogy

• An analogy is a way of understanding an idea by using a different but similar situation

• Rolling dice is a good analogy of radioactive decay because it is similar to the random nature of radioactive decay

A dice roll is a random process because you don't know when you will roll a particular value. However, you can determine the probability of a particular result

• Imagine someone rolling a dice and trying to get a ‘6’

• Each time they roll, they do not know what the result will be

• But they know there is a 1/6 probability that it will be a 6

• If they were to roll the dice 1000 times, it would be very likely that they would roll a 6 at least once

• The random nature of radioactive decay can be demonstrated by observing the count rate of a Geiger-Muller (GM) tube

  • When a GM tube is placed near a radioactive source, the counts are found to be irregular and cannot be predicted

  • Each count represents a decay of an unstable nucleus

  • These fluctuations in count rate on the GM tube provide evidence for the randomness of radioactive decay

The variation of count rate over time of a sample radioactive gas. The fluctuations show the randomness of radioactive decay

Half-Life

• It is impossible to know when a particular unstable nucleus will decay

• But the rate at which the activity of a sample decreases can be known

  • This is known as the half-life

• Half-life is defined as:

The time it takes for the number of nuclei of a sample of radioactive isotopes to decrease by half

OR

The time it takes for the count rate of a sample to fall to half its initial level

• In other words, the time it takes for the activity of a sample to fall to half its original level

• Count rate is the number of decays recorded each second by a detector, such as a Geiger–Müller (GM) tube

• Different isotopes have different half-lives and half-lives can vary from a fraction of a second to billions of years in length

Using Half-life

• Scientists can measure the half-lives of different isotopes accurately:

• Uranium-235 has a half-life of 704 million years

  • This means it would take 704 million years for the activity of a uranium-235 sample to decrease to half its original amount

• Carbon-14 has a half-life of 5700 years

  • So after 5700 years, there would be 50% of the original amount of carbon-14 remaining

  • After two half-lives, or 11 400 years, there would be just 25% of the carbon-14 remaining

• With each half-life, the amount remaining decreases by half

The diagram shows how the activity of a radioactive sample changes over time. Each time the original activity halves, another half-life has passed

• The time it takes for the activity of the sample to decrease from 100 % to 50 % is the half-life

• It is the same length of time as it would take to decrease from 50 % activity to 25 % activity

• The half-life is constant for a particular isotope

Calculating Half-Life

• To calculate the half-life of a sample, the procedure is:

  • Measure the initial activity, A₀, of the sample

  • Determine the half-life of this original activity

  • Measure how the activity changes with time

• The time taken for the activity to decrease to half its original value is the half-life

Calculating Radioactive Decay

Higher Tier Only

• Half-life is the time it takes for the number of nuclei of a sample of radioactive isotopes to decrease by half

• With each half-life, the activity of a sample decreases by half

• The ratio of remaining radioactive nuclei to the decayed nuclei after a period of time can be calculated in different ways

Method 1: Halving Method

• Determine the number of half-lives elapsed

• Multiply the number 1 by half for each half-life elapsed

• For example, if 4 half-lives have elapsed:

1 × ½ × ½ × ½ × ½ = 1 / 16

• This is the same as a ratio of 1 remaining : 16 original nuclei, or 1:16

Method 2: Raising to a Power

• Determine the number of half-lives elapsed

• Use your calculator to raise ½ to the number of half-lives

• For example, if 4 half-lives have elapsed:

(1/2)⁴ = 1/16

• This is the same as a ratio of 1 remaining : 16 original nuclei, or 1:16