Radioactive Decay (AQA A Level Physics)

Radioactive Decay

• Radioactive decay is defined as:

  The spontaneous disintegration of a nucleus to form a more stable nucleus, resulting in the emission of an alpha, beta or gamma particle

• 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 proportion of nuclei decaying in a given time period

• 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

Activity & The Decay Constant

• Since radioactive decay is spontaneous and random, it is useful to consider the average number of nuclei that are expected to decay per unit time

  • This is known as the average decay rate

• As a result, each radioactive element can be assigned a decay constant

• The decay constant λ is defined as:

   The probability that an individual nucleus will decay per unit of time

• When a sample is highly radioactive, this means the number of decays per unit time is very high

  • This suggests it has a high level of activity

• The activity A of a radioactive sample is defined as:

  The average number of nuclei that decay per unit of time

• It can be calculated using:

• Where:

  • A = activity of the sample (Bq)

  • ΔN = number of decayed nuclei

  • Δt = time interval (s)

  • λ = decay constant (s^-1)

  • N = number of nuclei remaining in a sample

• The activity of a sample is measured in Becquerels (Bq)

  • An activity of 1 Bq is equal to one decay per second, or 1 s^-1

• This equation shows:

  • The greater the decay constant, the greater the activity of the sample

  • The activity depends on the number of undecayed nuclei remaining in the sample

  • The minus sign indicates that the number of nuclei remaining decreases with time