Exponential Decay

• What is the process called when the number of undecayed nuclei falls rapidly?

  Exponential decay
• What shape does the graph of radioactive decay exhibit?

  A distinctive exponential shape
• What does a steeper slope on a decay graph indicate?

  A larger decay constant λ
• Where does the decay curve start on the graph?

  At the initial number of undecayed nuclei

  
• What is the equation for the number of undecayed nuclei N in exponential form?

  N = N e$–λt$

  
• What does N represent in the equation N = N e$–λt$?


  The initial number of undecayed nuclei

  
• What does λ represent in the equation for radioactive decay?

  The decay constant

  
• What is the unit for the decay constant λ?

  s$–1$
• How is activity A related to the number of undecayed nuclei N?

  A is directly proportional to N

  
• What is the equation for activity A in exponential form?

  A = A e$–λt$
• What does C represent in the equation C = C e$–λt$?


  The count rate at a certain time t
• What is the approximate value of the exponential constant e?

  Approximately 2.718
• What is the inverse function of e?

  ln(y), the natural logarithmic function
• What is the definition of molar mass?

  • Mass of a substance in grams in one mole
  • Unit: g mol$–1$

  
• What is the decay constant of Strontium-90?

  0.025 year$–1$
• How do you express the activity A of a sample after 5.0 years?

  A = A e$–λt$
• What fraction does the activity of Strontium-90 decrease by after 5 years?

  By a factor of 0.88
• What is Avogadro's constant?

  • Number of atoms in one mole
  • Equal to 6.02 × 10$23$ mol$–1$
• How many atoms are in one mole of sodium (Na)?

  6.02 × 10$23$ atoms
• What is the mass of americium-241 in the smoke detector?

  5.1 µg
• What is the initial activity level of americium-241 in smoke detectors?

  6.1 × 10$5$ Bq
• How do you calculate the number of nuclei in a sample?

  N = $\frac{mass \times N_A}{molar \, mass}$

  
• What is the decay constant λ of americium-241?

  4.65 × 10$–11$ s$–1$
• How old is the smoke detector?

  22.7 years
• What are the steps to determine the age of a smoke detector using activity?

  1. Write known quantities
  2. Use the equation A = A₀ e$–λt$
  3. Rearrange for time t
  4. Calculate age in years