RP: Inverse Square-Law for Gamma Radiation

• What is the aim of the experiment on gamma radiation?

  To verify the inverse square law
• What is the independent variable in the gamma radiation experiment?

  The distance between the source and detector

  
• What is the dependent variable in the gamma radiation experiment?

  The count rate / activity of the source
• What are the control variables in the gamma radiation experiment?

  • Time interval of each measurement
  • Thickness of aluminium foil
  • Gamma source used
  • GM tube used
• What is the resolution of a metre ruler used in the experiment?

  1 mm
• What is the resolution of the stopwatch used in the experiment?

  0.01 s
• What are the steps in the method for the inverse square law investigation?

  1. Measure background radiation with GM tube
  2. Place gamma source at a starting distance
  3. Measure counts in 60 seconds
  4. Record 3 measurements for each distance
  5. Repeat for several distances in 5 cm intervals
• According to the inverse square law, how does intensity relate to distance?

  Intensity is inversely proportional to distance squared
• What is the relationship between intensity and corrected count rate?

  Intensity is proportional to corrected count rate

  
• What does the equation $C \propto \frac{1}{x^2}$ represent?


  Corrected count rate is inversely proportional to distance squared
• What does the rearranged equation <latex{\frac{1}{C} = kx}</latex> indicate?

  It compares to the equation of a straight line
• What should be done to the background radiation readings?

  Subtract from each count rate reading
• What does a straight-line graph of <latex{\frac{1}{C}} </latex> against distance indicate?

  It confirms the inverse square relationship
• What does it mean if the graph does not go through the origin?

  It indicates a systematic error in measurement

  
• What are the main sources of systematic error in the experiment?

  • Measurement of distance inaccuracies
  • Detector and source positions unknown
  • Dead time in Geiger counter

  
• What is "dead time" in a Geiger counter?

  When multiple counts happen simultaneously
• How can the issue of dead time be reduced?

  By using a more modern Geiger counter
• Why should the Geiger-Muller tube be shielded with aluminium?

  To prevent alpha or beta radiation from being measured
• What are the random errors in the gamma radiation experiment?

  • Radioactive decay is random
  • Repeat readings are vital
  • Measure over the longest time span possible
  • Larger counts reduce statistical uncertainty
• How does the percentage error relate to count size?

  It is proportional to the inverse-square root of the count
• What safety considerations should be taken for the gamma source?

  • Reduce exposure time in lead-lined box
  • Handle with long tongs
  • Do not point source at anyone
  • Wear safety clothing (lab coat, gloves, goggles)
• What is the first step in analyzing the student's data for the inverse square law?

  Determine a mean value of background radiation
• How is the corrected average count rate calculated?

  By subtracting background radiation from total counts
• What is the formula for calculating uncertainty in the count rate?

  $\Delta C =$$\frac{1}{2} \times \text{range of repeat readings}$
• How is the uncertainty in the gradient calculated?

  <latex%\text{ uncertainty} = \frac{\text{worst gradient} - \text{best gradient}}{\text{best gradient}} \times 100%</latex>