1. 5.3.3 Radioactivity

2. (a) describe the spontaneous and random nature of radioactive decay of unstable nuclei

3. Will emit radiation randomly once
Radioactive decay
Stable
Unstable:
Will emit radiation randomly once

4. Radioactive decay Nuclear decay is spontaneous because:
the decay of a particular nucleus is not affected by the presence of other nuclei
the decay of nuclei cannot be affected by chemical reactions or external factors such as temperature and pressure
and is random because:
it is impossible to predict when a particular nucleus in the sample is going to decay
each nucleus in a sample has the same chance of decaying per unit time

5. (b) describe the nature, penetration and range of α-
(b) describe the nature, penetration and range of α- particles, β-particles and γ-rays

6. Radiation penetration
2 Protons
ALPHA
2 Neutrons
BETA
High Energy
Electron
GAMMA
ALUMINIUM
High
Frequency Wave
PAPER
LEAD

7. Radiation penetration
Type of decay:
What is emitted?
Description of
decay:
Example of decay:
Effect on A and Z:
Alpha decay
Alpha particle (helium nuclei)
2 neutrons and 2 protons are emitted from the nucleus.
U  Th +  + energy
A decreases by 4, Z decreases by 2
(A-4, Z-2)

8. Radiation penetration
Type of decay:
What is emitted?
Description of
decay:
Example of decay:
Effect on A and Z:
Beta decay
High energy electron
A neutron in the nucleus decays into a proton and a high energy electron which is emitted with an anti-neutrino.
C  N  ν
A stays the same, Z increases by 1
(A=, Z+1)

9. Radiation penetration
Type of decay:
What is emitted?
Description of
decay:
Effect on A and Z:
Gamma decay
High energy electromagnetic radiation
Nucleus loses energy and becomes more stable. Gamma radiation is the energy it loses.
A stays the same, Z stays the same
(A=, Z=)

10. (c) define and use the quantities activity and decay constant10

11. Activity
The activity of a source is defined as follows: Activity is measured in decays per second (or h-1 or day-1, etc) An activity of one decay per second is one becquerel (1 Bq) 1 Bq = 1 s-1
The activity A of a radioactive sample is the rate at which nuclei decay or disintegrate

12. Decay constant
The decay constant of a source is defined as follows: For example, in a sample of one million nuclei, if in one hour, then the decay constant is Decay constant λ = 0.20 h-1
The decay constant λ is the probability that an individual nucleus will decay per unit time interval

13. (d) select and apply the equation for activity A = λN13

14. Activity equation Activity of a sample depends on the decay constant λ
The greater the decay constant, the greater the activity
Activity also depends on the number of undecayed nuclei in the sample N
A = λN

15. Questions
A sample of carbon-15 initially contains undecayed nuclei. The decay constant for this isotope of carbon is 0.30 s-1. Determine the initial activity of the sample
A small sample of radium gives a received count rate of 20 counts per minute in a detector. It is known that the counter detects only 10% of the decays from the sample. The sample contains 1.5 x 109 undecayed nuclei. Determine the decay constant of this form of radium
A = λN
= 0.30 s-1 x
= s-1 or Bq
Count rate = 20 m-1 therefore 0.33 s-1
Activity = 3.3 s-1
Decay Constant = 3.3 s-1 / 1.5 x 109
= 2.0 x 10-9 s-1

16. (e) select and apply the equations A = Aoe-λt and N = Noe-λt where A is the activity and N is the number of undecayed nuclei 16

17. Decay equations 100 Undecayed Atoms [N] or Activity [A] (s-1) 50 14 2814 28
Time [t] (s)

18. Decay equations
The decay in the graph can be expressed as an equation If N0 is the number of undecayed nuclei, then N that remain undecayed after time t is given by: N = Noe-λt

19. Decay equations
The activity A of a sample is proportional to the number of undecayed nuclei N. Hence the activity of the sample decreases exponentially: A = Aoe-λt

20. Questions Now attempt SAQ 13, 14 and 15
Use Worked Example 5 & 6 for help

21. (e) define and apply the term half-life21

22. Half-life
100
Undecayed Atoms 50 14 28
Time (s)

23. Half-life
The half-life t½ of a radioisotope is the mean time taken for half of the active nuclei in a sample to decay

24. (g) select and use the equation λt1/2 = 0.69324

25. Decay constant and half-life
The decay constant and half-life are connected by the formula:
λt1/2 = 0.693

26. Assessment Chapter 14 SAQ’s 1 to 21 End of Chapter 14 questions 1 - 5
Radioactivity worksheet questions