Activity & The Decay Constant (OCR A Level Physics): Revision Note

Activity & The Decay Constant

• Since radioactive decay is spontaneous and random, it is useful to consider the average number of nuclei which 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, per second, that a given nucleus will decay

• 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

• Activity, or the number of decays per unit time 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 - however, for calculations it can be omitted