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A –Level Physics: Nuclear Decay
Half Life and Background Radiation
Objectives:
FLASHBACK
FLASHBACK: Compare and contrast electric and gravitational
fields (6 marks)
Starter Activity
Describe AND explain what
happens to the mass and
atomic number of an element
that undergoes the following:
1.
2.
3.
4.
Alpha Decay
Beta – Decay
Beta + Decay
Gamma Decay
Independent Study
Create a revision poster for the particle unit!
Rate of Decay
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?
1) The Isotope Involved
2) The number of undecayed nuclei
Mathematical Relationship
The relationship between the rate of decay (or activity) of an isotope
and the number of undecayed nuclei is given by:
-400BC
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
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
Mathematical Relationship
An alternative (and more common in the exam)
approach to express this relationship is:
-400BC
ΔN
= -λN
Δ𝑡
Which can be expressed in terms of the original activity
of time=0 :
-λt
N=N0e
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)
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.
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.
Half Life
The
-400BC
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:
This is equal to 0.693
Decay constant (s-1)
The half-life of one radioactive isotope of
sodium is 2.6 years. Show that its decay
constant is 8.4x10–9 s–1
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
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
2.
3.
To achieve this, you should do the following:
1. Take a starting activity (e.g. at time=0)
Determine half that value then go across to the curve and down to the xaxis. This is the half life
Do this again for another set of values and then work out an average half
life
Practice
Plot the following and determine the half life
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