Radioactive Decay (Radioactivity II)

Activity The unit of activity is the becquerel (Bq), defined

as one disintegration per second: 1 Bq = 1 s 1.

The traditional unit of activity is the curie (Ci),

which was originally the activity ascribed

to 1 g of 226Ra.

The curie is now defined as 1 Ci = 3.71010 Bq,

exactly

Exponential Decay

Exponential Decay

Since the activity of a sample and the number

of atoms present are proportional, activity

follows the same rate of decrease,

Exponential radioactivity decay law, showing relative

activity, A/A0, as a function of time t and

T the half-life.

Half Life

Example

Solution

Mean Lifetime The mean lifetime , "tau" the average life

time of a radioactive particle before decay.

Time constant and mean-life

For the one-decay solution :

Mean Lifetime

Mean Lifetime This form is also true for two-decay processes

simultaneously , inserting the

equivalent values of decay constants (as given a

bove):

into the decay solution leads to:

Specific Activity Number of decays per unit time per amount of

substance of the sample at time set to zero (t =

0). "Amount of substance" can be the mass,

volume or moles of the initial sample

Specific Activity Mass of the radionuclide is given by

where m is mass number of the radionuclide

and NA is Avogadro constant.

Specific radioactivity S is defined as radioactivity

per unit mass of the radionuclide:

Specific Activity In addition, decay constant is related to the half-

life T1/2 by the following equation:

This equation is simplified by

, When the unit of half-

life converts a year

Specific Activity For example, specific radioactivity of radium

226 with a half-life of 1600 years is obtained by

This value derived from radium 226 was defined

as unit of radioactivity known as Curie (Ci)

Decay Probability for a Finite Time

Interval

Decay by Competing

Processes Some radionuclides decay by more than one

process. For example:

The decay constants for the three decay modes

are + = 0.009497 h-1, - = 0.02129 h

-1 and

EC = 0.02380 h-1.

Decay by Competing

Processes To find the effective decay constant when the

decay process has n competing decay modes,

write the differential equation that models the

rate of decay.

Denote the decay constant for the ith mode by

i. Thus, the rate of decay of the parent

radionuclide is given by,

Decay by Competing

Processes

where A is the overall decay constant, namely,

The probability fi that the nuclide will decay by

the ith mode is

Example What is the probability 64Cu decays by positron

emission? The decay constants for the three

decay modes are + = 0.009497 h-1, - =

0.02129 h-1 and EC = 0.02380 h-1.

Solution

Solution

a value in agreement with the branching

probabilities is: