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: 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

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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

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

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. antiquarks

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. antiquarks

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) antiquarks 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 antiquarks

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 antiquarks

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 5.1 x 10-10 N