AQA A Level Physics

Revision Notes

8.2.1 Radioactive Decay

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

Radioactivity Fluctuations, downloadable AS & A Level Physics revision notes

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
  • Activity, or the number of decays per unit time can be calculated using:

Activity & The Decay Constant equation 1

  • 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

Worked Example

Radium is a radioactive element first discovered by Marie and Pierre Curie. They used the radiation emitted from radium-226 to define a unit called the Curie (Ci) which they defined as the activity of 1 gram of radium.

It was found that in a 1 g sample of radium, 2.22 × 1012 atoms decayed in 1 minute.

Another sample containing 3.2 × 1022 radium-226 atoms had an activity of 12 Ci.

a) Determine the value of 1 Curie

b) Determine the decay constant for radium-226

Part a)

Step 1: Write down the known quantities

    • Number of atoms decayed, ΔN = 2.22 × 1012
    • Time, Δt = 1 minutes = 60 s

Step 2: Write down the activity equation

Step 3: Calculate the value of 1 Ci

Part b)

Step 1: Write down the known quantities

    • Number of atoms, N = 3.2 × 1022
    • Activity, A = 12 Ci = 12 × (3.7 × 1010) = 4.44 × 1011 Bq

Step 2: Write down the activity equation

A = λN

Step 3: Calculate the decay constant of radium

    • Therefore, the decay constant of radium-226 is 1.4 × 10–11 s–1
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