Episode 515: The Radioactive Decay
Episode 515: The radioactive decay formula
Here, the key idea is the random nature of the decay. Avoid simply pulling pull equations out of the air – at least make them plausible.
Summary
Discussion: The meaning of the decay constant λ. (15 minutes)
Discussion: The link with half-life. (15 minutes)
Student experiments: Analogue experiments linking probability with decay rates. (20 minutes)
Discussion:
The meaning of the decay constant λ.
Start from the definition of the decay constant λ: the probability or chance that an individual nucleus will decay per second. (You may like to comment on the problem with notation in physics. λ is used for wavelength as well as the decay constant. The context should make it unambiguous.)
Units: λ is measured in s-1 (or h-1, year-1, etc).
If you …show more content…
colouring three faces red gives a chance of a red face being uppermost representing decay has a probability of decay of ½; colour two faces blue (chance of decay = 2 x 1/6 = 1/3), and one face yellow (chance of decay 1/6). Sugar cubes can be used, painted with food colouring.
Throw drawing pins: decay = point upwards. Safety: beware sharp points!
Is the chance of decay = ½?
The drop in height of the head on a glass of beer usually shows exponential behaviour – opportunity for a field trip?
Water flowing out through a restriction: at any instant the water remaining represents the undecayed nuclei; the water that has flowed out represents the decayed nuclei. Flow rate depends upon the pressure head ~ the height of water remaining ~ quantity of water remaining.
TAP 515-1: Smoothed out radioactive decay
Here is the first step in making a model – idealisation and simplification of a messy process
[pic]
Practical advice
The diagram could be used for an
Here, the key idea is the random nature of the decay. Avoid simply pulling pull equations out of the air – at least make them plausible.
Summary
Discussion: The meaning of the decay constant λ. (15 minutes)
Discussion: The link with half-life. (15 minutes)
Student experiments: Analogue experiments linking probability with decay rates. (20 minutes)
Discussion:
The meaning of the decay constant λ.
Start from the definition of the decay constant λ: the probability or chance that an individual nucleus will decay per second. (You may like to comment on the problem with notation in physics. λ is used for wavelength as well as the decay constant. The context should make it unambiguous.)
Units: λ is measured in s-1 (or h-1, year-1, etc).
If you …show more content…
colouring three faces red gives a chance of a red face being uppermost representing decay has a probability of decay of ½; colour two faces blue (chance of decay = 2 x 1/6 = 1/3), and one face yellow (chance of decay 1/6). Sugar cubes can be used, painted with food colouring.
Throw drawing pins: decay = point upwards. Safety: beware sharp points!
Is the chance of decay = ½?
The drop in height of the head on a glass of beer usually shows exponential behaviour – opportunity for a field trip?
Water flowing out through a restriction: at any instant the water remaining represents the undecayed nuclei; the water that has flowed out represents the decayed nuclei. Flow rate depends upon the pressure head ~ the height of water remaining ~ quantity of water remaining.
TAP 515-1: Smoothed out radioactive decay
Here is the first step in making a model – idealisation and simplification of a messy process
[pic]
Practical advice
The diagram could be used for an