1. Press for Apollo13 Youtube clip Houston we have a problem 3.22 minutes
Many pictures thanks to NASA

2. Apollo 13 lost a lot of Oxygen when a tank exploded and another leaked

3. The astronauts survived by conserving electricity and oxygen as they lived in the Landing Module

4. It is obviously vital that spaceships carrying humans do not lose the oxygen to breathe
Apollo 15 had a small leak on the Moon.
3 Cosmonauts died on Soyuz 11 when a valve accidently opened in space

5. The Space Shuttle was always checked for leaks when the door was used.

6. Most of spaceships leak a little and spare oxygen is carried to top them up
Spheres are good for carrying high pressure gases as they have no stress concentrations in corners

7. Leaks worry space walkers
Micrometeoroid strike O O
Survive about 15 seconds
Saliva would boil (NOT blood)
Lack of oxygen to brain
Flesh expands to about twice the size
If breathe is held lungs will be damaged O O O O O O O

8. Where does radiation come from?
RECAP FROM Y11:
Where does radiation come from?
What is it?

9. What is this? Where does this pattern come from?

10. What factor affects what is changing
You get an exponential when the rate of change depends on how much you’ve got
Examples:
Radioactivity
(Capacitors – more on this in a couple of lessons time)
Water leaking out of a bucket
Air coming out of a tyre
Businesses expanding
Population explosion
For each one:
What is changing
What factor affects what is changing

11. In maths speak the idea that ‘the rate of change depends on how much you have left’ is written as:
dN = kN
Amount left
Rate of change dt
A constant that describes how quickly the exponential goes up (if it is positive) or goes down (if it is negative). It is the probability of increase or decay each second.
This is called a Differential equation (you might recognise the notation from maths).
You can write one of these for anything which follows an exponential pattern.
What would k be in the case of the dice?

12. dN = -N dt If we write one for radioactivity we could write:
Number of nuclei left
Rate of decay dt
This constant is called the decay constant.
Hand out card sort for students to summarise the difference between decay constant and half life.

13. So we actually have two things that measure the same thing – how fast is the decay happening?
t1/2
Decay constant
Measured in s-1 although occasionally min-1 or similar
Probability of nuclei decaying each second
Features in differential equation
Half life
Measured in s or other time units
Time it takes for the number of undecayed nuclei to half
Easy to work out from the decay graph
All true exponentials have a constant half life – we sometimes use them to check this

14. Link with half life? If you have a high probability of decay,
what effect does that have on the half
life?
They are inversely proportional.

15. t1/2 = ln 2  It might be handy if we could convert between them…
You can!
A number equal to 0.693
t1/2 = ln 2 
Half life
Decay constant.
They are inversely proportional to each other. The proportionality constant is ln 2.
ln stands for Natural Logarithm which we will come back to later.

16. Example The decay constant of a radioactive
isotope of strontium is 7.84 x s-1.
What is the half life?
28 years

17. 1. Finding half life
The graph shows the decay of a radioactive nuclide.
QOTD
Determine the half-life of this radionuclide.

18. 2. Calculating decay constant
Carbon-14 has a half-life of 5600 years.
Calculate the decay constant of
carbon-14.

19. 3. Half life The half-life of caesium-137 is 30 years.
When the fuel rods are removed from a
nuclear reactor core, the total activity of
the caesium-137 is 6.4 × 1015 Bq.
Q. After how many half-lives will this
activity have fallen to 2.5 × 1013 Bq?
Show your working

20. 4. Decay constant An alpha particle source of half life 3420
years has a rate of decay of 450kBq.
Calculate the decay constant in s-1
Calculate the number of radioactive atoms in the source initially.

21. Practise Questions A radioactive isotope has a half
life of 35 years. A fresh sample
of this isotope has an activity of
25kBq.
Calculate the decay constant in s -1
The activity after 10 years.

22. Exam question (from last lesson)
Begin 2nd lesson of session with this?

23. The End!  = ln 2 t1/2  = 1.3×10-5 the probability per second (1)
of the decay of a (single) nucleus/atom (1)
The End!