Radioactive Decay

Nuclear Physics Lesson 5

Learning ObjectivesLearning 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 Explain what is meant by the activity of a radioactive isotope.radioactive isotope.

Calculate the activity of a radioactive Calculate the activity of a radioactive sample after an integer number of half-sample after an integer number of half-lives. lives.

Interpret graphical and numerical data of Interpret graphical and numerical data of radioactive decay.radioactive decay.

What is radioactive What is radioactive decay?decay?

Radioactive DecayRadioactive Decay

It’s really all about unstable isotopes It’s really all about unstable isotopes changing to stable isotopes.changing to stable isotopes.

It is random.It is random.

One element is changing into One element is changing into another...and an another...and an αα or a or a ββ particle is particle is emitted.emitted.

What is Half-Life?What is Half-Life?

Half-LifeHalf-Life

From Wikipedia...From Wikipedia...

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

Half-LifeHalf-Life

The The half-lifehalf-life, T, T1/21/2, of a radioactive isotope , of a radioactive isotope is the time taken for the mass of the is the time taken for the mass of the isotope to decrease to half the initial mass.isotope to decrease to half the initial mass.

If the half-life is very long then the If the half-life is very long then the substance will remain radioactive for a substance will remain radioactive for a very long time.very long time.

If the half life is short it will decay quickly If the half life is short it will decay quickly

Modelling RadioactivityModelling Radioactivity

Roll all of the dice.Roll all of the dice. Remove all the dice with a cross facing Remove all the dice with a cross facing

upwards.upwards. Record how many dice are left in a Record how many dice are left in a

table.table. Repeat 20 times.Repeat 20 times.

Plot dice remainingPlot dice remaining vs. no. of throwsvs. no. of throws

Already know what Already know what happens?happens?

Let’s try an alternative method:-Let’s try an alternative method:- Plot ln(N) vs. tPlot ln(N) vs. t where t = number of throws.where t = number of throws. and N = number of dice remaining after t and N = number of dice remaining after t

throws.throws. The relationship between N and t is given by:The relationship between N and t is given by: where where λλ is the decay is the decay

constant.constant. and Nand N00 is the initial is the initial

number number of dice. of dice. teNN 0

A ChallengeA Challenge

Show that a plot of ln(N) vs. t will Show that a plot of ln(N) vs. t will produce a straight line with a produce a straight line with a gradient = -gradient = -λλ and an intercept=ln and an intercept=ln NN00..

Show that half life, TShow that half life, T1/21/2 can be given can be given by the equation:-by the equation:-

2ln

2/1 T

Challenge Help...Challenge Help...

Log both sides:-Log both sides:-

Flipping within the ln function on the Flipping within the ln function on the left side:-left side:-

After one Half-Life N/NAfter one Half-Life N/N00 = 0.5 and so:- = 0.5 and so:-

tN

N

0ln

tN

N

0

ln

2/12ln T

Decay CurveDecay Curve

Extension Work...Extension Work...

ActivityActivity

The The activityactivity, A ,of a radioactive isotope , A ,of a radioactive isotope is the number of nuclei of the isotope is the number of nuclei of the isotope that disintegrate per second.that disintegrate per second.

Activity is measured in Becquerels (Bq) Activity is measured in Becquerels (Bq) which is the number of decays per which is the number of decays per second.second.

time(s)

decays ofnumber totalq)activity(B

Half-Life IIHalf-Life II

The time it takes the activity of a The time it takes the activity of a radioactive sample to decreases radioactive sample to decreases

The time it takes the count rate from a The time it takes the count rate from a radioisotope to decrease by 50%.radioisotope to decrease by 50%.