Radioactive Decay Nuclear Physics Lesson 5

Learning Objectives Explain what is meant by the term half-life. Explain what is meant by the term half-life. Explain what is meant by the activity of a radioactive isotope. Explain what is meant by the activity of a radioactive isotope. Calculate the activity of a radioactive sample after an integer number of half-lives. Calculate the activity of a radioactive sample after an integer number of half-lives. Interpret graphical and numerical data of radioactive decay. Interpret graphical and numerical data of radioactive decay.

What is radioactive decay?

Radioactive Decay It’s really all about unstable isotopes changing to stable isotopes. It’s really all about unstable isotopes changing to stable isotopes. It is random. It is random. One element is changing into another...and an α or a β particle is emitted. One element is changing into another...and an α or a β particle is emitted.

What is Half-Life?

Half-Life From Wikipedia... Half-Life is a science fiction first-person shooter video game developed by Valve Software and the company's debut product.science fictionfirst-person shootervideo gameValve Software

Half-Life The half-life, T 1/2, of a radioactive isotope is the time taken for the mass of the isotope to decrease to half the initial mass. The half-life, T 1/2, of a radioactive isotope is the time taken for the mass of the isotope to decrease to half the initial mass. If the half-life is very long then the substance will remain radioactive for a very long time. If the half-life is very long then the substance will remain radioactive for a very long time. If the half life is short it will decay quickly If the half life is short it will decay quickly

Modelling Radioactivity Roll all of the dice. Roll all of the dice. Remove all the dice with a cross facing upwards. Remove all the dice with a cross facing upwards. Record how many dice are left in a table. Record how many dice are left in a table. Repeat 20 times. Repeat 20 times. Plot dice remaining Plot dice remaining vs. no. of throws vs. no. of throws

Already know what happens? Let’s try an alternative method:- Let’s try an alternative method:- Plot ln(N) vs. t Plot ln(N) vs. t where t = number of throws. where t = number of throws. and N = number of dice remaining after t throws. and N = number of dice remaining after t throws. The relationship between N and t is given by: The relationship between N and t is given by: where λ is the decay constant. where λ is the decay constant. and N 0 is the initial number of dice. and N 0 is the initial number of dice.

A Challenge Show that a plot of ln(N) vs. t will produce a straight line with a gradient = -λ and an intercept=ln N 0. Show that a plot of ln(N) vs. t will produce a straight line with a gradient = -λ and an intercept=ln N 0. Show that half life, T 1/2 can be given by the equation:- Show that half life, T 1/2 can be given by the equation:-

Challenge Help... Log both sides:- Log both sides:- Flipping within the ln function on the left side:- Flipping within the ln function on the left side:- After one Half-Life N/N 0 = 0.5 and so:- After one Half-Life N/N 0 = 0.5 and so:-

Decay Curve

Extension Work...

Activity The activity, A,of a radioactive isotope is the number of nuclei of the isotope that disintegrate per second. The activity, A,of a radioactive isotope is the number of nuclei of the isotope that disintegrate per second. Activity is measured in Becquerels (Bq) which is the number of decays per second. Activity is measured in Becquerels (Bq) which is the number of decays per second.

Half-Life II The time it takes the activity of a radioactive sample to decreases The time it takes the activity of a radioactive sample to decreases The time it takes the count rate from a radioisotope to decrease by 50%. The time it takes the count rate from a radioisotope to decrease by 50%.