The-Kinetics-of-Radioactive-Decay-Lesson-6.pptx - The...

The
Kinetics of
Radioactive
Decay
LESSON 6

The Kinetics of Radioactive Decay
includes:
 Calculations Using the First Order Rate Equation:
r = k [N]
Since the rate of radioactive decay is first order we can say:
r = k [N]
 Determination of the Rate Constant, k
 Determination of the Activity

What is the rate constant of
radioactive decay, k?
 Radioactive decay obeys a first-order rate law, meaning
that the rate (A) is directly proportional to the number of
reactant (radionuclide) atoms/molecules at any given
time:

A = kN

k is called a rate constant or specific activity

k = rate of decay / N

Calculations Using the First Order Rate
Equation: r = k[N]
Since the rate of radioactive decay is first order we can say:
r = k[N]
1
,
where r is a measurement of the rate of decay,
k is the first order rate constant for the isotope, and
N is the amount of radioisotope at the moment when the rate is measured
.

The rate of decay is often referred to as the activity of the isotope and is often measured in Curies
(Ci),
 one curie = 3.700 x 10
10
atoms that decay/second.
 By knowing the amount of radioisotope and the activity of the sample, the rate constant can be
determined.

Determination of the Rate Constant
 Example: A 1.00 g sample of cobalt-60 (59.92 g/mol) has an
activity of 1.1 x 10
3
Ci. Determine the rate constant.
 First, we need to convert the 1.00 g of sample into number of atoms
of cobalt-60 and to convert the activity into numbers of atoms that
decay per second.
No. of atoms Co = weight divided by At. Mass times Avog. No.
= (1.00 g )(1 mol /59.92 g)(6.022 x 10
23
atoms Co-60/mol)
no. of atoms of Co = 1.01 x 10
22
atoms

Cont.
Since rate of activity is in Ci, (1.1 x Ci) express this to atoms
one curie = 3.700 x 10
10
atoms that decay/second
r = (1.1 x 10
3
Ci)(3.700 x 10
10
atoms/s/Ci)
= 4.1 x 10
13
atoms that decay/sec
