1. A –Level Physics: Nuclear Decay Half Life and Background Radiation

2. Objectives:

3. FLASHBACK
FLASHBACK: Compare and contrast electric and gravitational fields (6 marks)

4. Starter Activity
Describe AND explain what happens to the mass and atomic number of an element that undergoes the following:
Alpha Decay
Beta – Decay
Beta + Decay
Gamma Decay
Alpha= Mass number goes down by 4 and atomic by 2 as it’s 2 protons and 2 neutrons
Beta - = Unchanged the mass, as a neutron changes to a proton, the atomic number goes up by 1
Beta + = Unchanged mass, as a proton changes to a neutron, the atomic number goes down by 1
Gamma= unchanged all

5. Independent Study
Create a revision poster for the particle unit!

6. Which two factors would determine the rate of decay of a sample?
The activity (or rate of decay) of a sample is measured in becquerel (Bq). An activity of 1Bq represents a rate decay of 1 per second.
Radioactive decay is known as a random process as the decay of an individual nucleus cannot be predicted. However, given a sample containing large numbers of undecayed nuclei, then statistically the rate of decay should be proportional to the number of undecayed nuclei present
Which two factors would determine the rate of decay of a sample?
The Isotope Involved
The number of undecayed nuclei

7. Mathematical Relationship
The relationship between the rate of decay (or activity) of an isotope and the number of undecayed nuclei is given by:
Activity (A) = λN or 𝑁 𝑡
Whereby λ is the decay constant of the isotope (unit of s-1) and N is the number of undecayed nuclei present
-400BC
If the activity/count is plotted against time you’ll notice two things:
The gradient is proportional to y
In intervals of x, the value of y changes in the same ratio
This is called an exponential curve
antiquarks

8. Mathematical Relationship
An alternative (and more common in the exam) approach to express this relationship is:
ΔN Δ𝑡 = -λN
Which can be expressed in terms of the original activity of time=0 :
N=N0e-λt
N0 = number of undecayed nuclei at t=0 t = time after t=0 in seconds N = the number of undecayed nuclei at time t λ= decay constant (s-1)
-400BC
The decay constant for caesium-137 is 7.3x10–10 s–1.
Calculate the number of atoms in a sample of caesium-137 that has an activity of
2.0 x 105 Bq.
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9. Mathematical Relationship
-400BC
The decay constant for caesium-137 is 7.3x10–10 s–1.
Calculate the number of atoms in a sample of caesium-137 that has an activity of
2.0 x 105 Bq.
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10. Half Life
The half life of a radioactive isotope (t½) is the average time taken for the number of undecayed nuclei of the isotope to halve
The half life of an isotope and its decay constant are related by the equation:
-400BC
This is equal to 0.693
Decay constant (s-1)
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The half-life of one radioactive isotope of sodium is 2.6 years. Show that its decay constant is 8.4x10–9 s–1

11. Half Life
-400BC
The half-life of one radioactive isotope of sodium is 2.6 years. Show that its decay constant is 8.4x10–9 s–1
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12. Half Life- Graphical Method
Sometimes in an exam it is possible to work out the half life using a graphical method whereby you are either given an exponential curve or need to plot the data first and subsequently determine the half life from the resulting curve
To achieve this, you should do the following:
Take a starting activity (e.g. at time=0)
Determine half that value then go across to the curve and down to the x-axis. This is the half life
Do this again for another set of values and then work out an average half life
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13. Practice
Plot the following and determine the half life

14. Exam Question
Complete the exam practice provided. Use all your notes to help. I will assist you through the questions only once all are attempted and when you have marked your answers according to the mark scheme.
NOTES: show all your workings and pattern of thought, do not be vague
5.1 x N