8.2.1 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

• 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:

• 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

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