Half-Life

• What is half-life defined as?

  The average time for nuclei to halve

  
• What happens to the activity of a sample after one half-life?

  The activity of the sample halves
• What is the relationship between activity and undecayed nuclei?

  Activity is proportional to undecayed nuclei
• What occurs to the activity after two half-lives?

  Activity falls to a quarter of the initial value

  
• What is the equation for exponential decay?

  N = N₀ e^-λt
• What does N represent in the exponential decay equation?

  The number of nuclei remaining in a sample

  
• What does N₀ represent in the exponential decay equation?

  The initial number of undecayed nuclei

  
• What does λ represent in the exponential decay equation?

  The decay constant
• How is half-life related to the decay constant?

  Half-life and decay constant are inversely proportional
• If the half-life is shorter, what can be said about the decay constant?

  The decay constant is larger
• What is the half-life of Strontium-90?

  28.0 years
• How do you convert the half-life of Strontium-90 into seconds?

  Multiply by 28 × 365 × 24 × 60 × 60
• What is the decay constant λ for Strontium-90?

  λ = 7.87 × 10^-10 s^-1
• How can the half-life of a radioactive substance be determined?

  From decay curves and log graphs

  
• What is the method to find half-life from decay curves?

  Draw a line to where activity halves

  
• Why are log graphs useful for interpreting decay data?

  They provide a straight-line plot
• What is the equation after taking natural logs of the exponential decay equation?

  ln N = ln(N₀) - λt

  
• What does the gradient of the log graph represent?

  The decay constant λ
• How do you determine the decay constant from a graph?

  By finding the gradient of the line
• How do you convert the half-life of technetium into seconds?

  t = 6 × 60 × 60
• How do you calculate the decay constant for technetium?

  Using the half-life equation

  
• How do you find the activity after 24 hours for technetium?

  By drawing lines on the graph

  
• What is the activity of technetium at t = 24 hours?

  A = 0.5 × 10⁷ Bq
• How do you calculate the number of technetium atoms remaining?

  Using the activity equation A = λN
• What is the activity equation?

  A = λN
• How do you find the number of atoms remaining in the sample?

  By rearranging the activity equation