Date your book and collect a container of dice from
the front
Count the total number of dice
Roll all the dice in one go. Set aside the dice
with dots facing up, count the dice without dots and record that
value.
Roll all the dice in one go that did did not land
with dots facing up. Discard those with dots facing up, count, record
and repeat until no dice remain.
Create a line graph showing the number of dice
rolled (y-axis) vs the trial number (x-axis)
What you have graphed is an exponential decay curve! This is what
nature does - we can observe it all over the place, even in electrical
circuits.
It is not important to understand why at the moment, just to
know that it does occur.
Mahi Tuatahi 2
A Carbon-14 nucleus emits a beta particle, then the
daughter nucleus also emits a beta particle immediately after. Write two
equations to show this.
An Uranium-241 nucleus emits an alpha particle AND
a beta particle. Write down the equation.
An atom of Carbon-11 absorbs a neutron. Write down
the nuclear equation.
The half-life is the time taken for half of the undecayed atoms in a
sample to decay.
Radioactive materials have unique half-lives.
It is impossible to predict when an
unstable/radioactive atom will disintegrate (decay), because the actual
timing of the decay is random.
Tauira
A small sample of a radioactive material iodine-131 has been observed
for several days while it decayed into xenon-131. Read the below and
determine its half-life.
On the first day, the sample contained 40,000
iodine-131 nuclei.
Eight days later, the sample only had 20,000
iodine-131 nuclei left.
Another eight days later, the sample had 10,000
iodine-131 nuclei left.
Iodide-131 Half-Life Graph
Pātai Tahi
The half-life of Hydrogen-3 is approximately 12.25 years. If you
found a small sample of Tritium containing 5,000,000 undecayed
nuclei.
How many nuclei will be left after 12.25 years
How many nuclei will be left after 24.5 years
How many nuclei will be left after 49 years
How many nuclei will be left after 196 years
How long until there is less than 2500 undecayed
nuclei left?
Whakatika Tahi
2,500,000
1,250,000
312,500
76.29
Between 10-11 half-lives
Akoranga 8 Mahi Tuatahi
You found a \(50 g\) sample of
Cobalt-60. The half-life of Cobalt-60 is 5 years. What would be the mass
of the Cobalt-60 sample after 20 years?
Estimate how long it would take for the mass of the
50 g sample to fall just below \(1.17
g\).
Sketch a mass vs. time graph of the Cobalt-60
sample over a 30-year period.
Use the graph to estimate the mass of the sample
after 12.5 years.
Exponential Decay
Curves
An exponential decay curve flattens out over
time
For any section, the graph is steeper on the left
than the right
This means, the mass/activity/number of atoms is
changing more rapidly on left than the right
