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Radioactive Decay

Physics: AQA A Level, topic 8.1.4

Radioactive Decay

When an object is radioactive it releases radioactive particles but as time passes the rate of particles decreases. This is called decay.

Random decay

Random decay

  • The decay of a radioactive substance is random and spontaneous.
  • To measure decay, we must look at the count rate over a long time to see if it decreases.
Probability

Probability

  • The probability that a given nucleus will decay in a given time is proportional to the number of nuclei. The equation for calculating the rate of decay is:
  • The rate of decay of nuclei = decay constant x the number of nuclei
  • ΔNΔt=−λN\frac{{\Delta}N}{{\Delta}t}=-{\lambda}N
    • λ{\lambda} is the decay constant.
    • NN is the number of nuclei.

The Exponential Law

The reduction in the rate of decay decreases according to an exponential pattern.

Exponential decay

Exponential decay

  • From the equation for the rate of decay, we can find an exponential relationship between the number of nuclei and time.
  • The equation for the rate of decay of nuclei is:
  • ΔNΔt=−λN\frac{{\Delta}N}{{\Delta}t}=-{\lambda}N
  • The exponential relationship corresponding to this is:
  • N=N0e−λtN={N_0}e^{-{\lambda}t}
    • N0{N_0} is the initial number of nuclei.
Activity

Activity

  • The activity of a sample can be found by using the decay constant and the number of nuclei. The equation for activity is:
  • Activity = decay constant x number of nuclei
  • A=λNA={\lambda}N
  • The exponential relationship corresponding to the activity is:
  • A=A0e−λtA={A_0}e^{-{\lambda}t}

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