Radioactive Decay
Objectives
- Model radioactive decay by rolling dice
- Measure the half-life of a radioactive material
- Show that radioactive flux decreases proportionally to distance squared.
Resources
- Dice and plastic tub
- Geiger counter
- Smoke alarm source (Americium-241)
- Barium-137 (provided by instructor) and glass slide
Background
Unstable atomic nuclei may undergo radioactive decay by emitting an alpha particle, a beta particle, or a gamma ray. Exactly when this will happen for a given particle is highly unpredictable, but for a large number of radioactive nuclei the number of decay events per unit time or activity A will be proportional to the total number of nuclei present: A\equiv\frac{\Delta N}{\Delta t} = \lambda N where the decay constant \lambda is specific to each isotope.
It can be shown that the activity and number of particles vs. time will both follow the same exponential curve: \frac{A}{A_0} = \frac{N}{N_0} = e^{-\lambda t} where A_0 and N_0 are the activity and number of particles at t=0, respectively.
A geiger counter is a robust and inexpensive device for detecting decay events from a radioactive source. It will, however, only detect the fraction of emitted radioactive particles that actually pass through the Geiger-Muller tube. Because radioactive particles are in general released in random directions from any source, the detection rate will be proportional to 1/d^2, where d is the distance from the source.
Guideposts/Hints
show/hide- When plotting an exponential relationship, the constant in the exponent can usually be found more easily by making a log-log plot and finding the slope of a linear fit to the data.