12.10 The Radioactive Decay Law

Question 1

What is the radioactive decay law?

Answer 1

The rate of decay of a nucleus is proportional to the number N of nuclei present that have not yet decayed dN/dt = -lambdaN

Question 2

What is the decay constant lambda ?

Answer 2

The probability of decay per unit time.

Question 3

What is the activity A?

Answer 3

The number of decays per second, the initial activity is Ao = lambdaNo.

Question 4

What is half life?

Answer 4

The time taken for the activity of a sample to halve.

Question 5

What does the radioactive decay law imply?

Answer 5

N = Noe^(-lambdat) and 
A = lambdaNoe^(-lambdat) thus the number of nuclei that have not yet decayed after time t and the activity after time t are both given by exponential decay laws.

Question 6

Since after one half life the initial activity of a sample is reduced by a factor of 2 and the decay constant and half life are related by lambaT1/2 = ln2 what can be derived?

Answer 6

A = Aoe^(-lambdat) 
Ao/2 = Aoe^(-lambdaT1/2)
e^(-lambdaT1/2) = 1/2
lambdaT1/2 = ln2

Question 7

What can we determine is we know the molar mass of a pure radioactive sample?

Answer 7

No the number of nuclei present by measuring the mass of the sample. Measuring the initial activity Ao then allows determination of the decay constant (through Ao = lambdaNo) and hence the half life (through lambdaT1/2 = ln 2). This method is useful for detaining very long half lives.