The Mystery of
Half- Life and Rate of
Decay
BY CANSU TÜRKAY
10-N
The truth is out there...
Before we start....
-
At the end of this presentation, you will be a
genious about these fallowing issues (at least
I hope so ) :
Conservation of Nucleon Number
Radioactive (a type of exponentional) Decay
Law and its Proof
Concept of Half- life
How to solve half-life problems
Conservation of....
 All three types of radioactive decays
(Alfa, beta and gamma) hold classical
conservation laws.
 Energy, linear momentum, angular
momentum, electric charge are all
conserved
Conservation of...
 The law of conservation of nucleon
number states that the total number of
nucleons (A) remains constant in any
process, although one particle can
change into another ( protons into
neutrons or vica versa). This is accepted
to be true for all the three radioactive
decays.
Radioactive Decay Law
and its Proof
 Radioactive decay is the spontaneous
release of energy in the form of
radioactive particles or waves.
 It results in a decrease over time of the
original amount of the radioactive
material.
Radioactive Decay Law
and its Proof
 Any radioactive isotope consists of a vast
number of radioactive nuclei.
 Nuclei does not decay all at once.
 Decay over a period of time.
 We can not predict when it will decay, its
a random process but...
6
Radioactive Decay Law
and its Proof
 ... We can determine, based on
probability, approximately how many
nuclei in a sample will decay over a given
time period, by asuming that each
nucleus has the same probability of
decaying in each second it exists.
7
Exponentional Decay
 A quantity is said to be subject to
exponentional decay if it decreases at a
rate proportional to its value.
8
Exponentional Decay
 Symbolically, this can be expressed as
the fallowing differential equation where
N is the quantity and λ is a positive
number called the decay constant:
 ∆N = - λN
∆t
Relating it to radioactive
decay law:
 The number of decays are represented
by ∆N
 The short time interval that ∆N occurs is
represented by ∆t
 N is the number of nuclei present
 λ is the decay constant
10
Relating it to radioactive
decay law:
 Here comes our first equation AGAIN, try
to look it with the new perspective:
 ∆N = - λN
∆t
11
What was that?!!!
 In the previous equation you have seen a
symbol like: λ
 λ is a constant of proportionality, called the
decay constant.
 It differs according to the isotope it is in.
 The greater λ is, the greater the rate of decay
 This means that the greater λ is, the more
radioactive the isotope is said to be.
12
Still confused about the
equation...
 Don’t worry! If you are still confused about
why this equation is like this, here is some
of the important points....
Confused Minds...
 With each decay that occurs (∆N) in a
short time period (∆t),a decrease in the
number N of the nuclei present is
observed.
 So; the minus sign indicates that N is
decreasing.
14
Got it!!!!
 Now, here is our little old equation:
 ∆N = - λN
POF!!!
∆t
 Now it has become the radioactive decay law!
(yehu)
What was that???
 N0 is the number of nuclei present at time
t=0
 The symbol e is the natural expoentional (as
we saw in the topic logarithm)
16
So what?
 Thus, the number of parent nuclei in a
sample decreases exponentionally in
time
 If reaction is first order with respect to [N],
integration with respect to time, t, gives
this equation.
17
As seen in the figure
below…
Please just
focus on how it
decays
exponetionally.
Half-life will be
discussed
soon…
HALF-LIFE
 The amount of time required for one-half
or 50% of the radioactive atoms to
undergo a radioactive decay.
 Every radioactive element has a specific
half-life associated with it.
 Is a spontaneous process.
HALF-LIFE
Ooops!!!
 Remember the first few slides? We
stated that we can not predict when
particular atom of an element will decay.
However half-life is defined for the time at
which 50% of the atoms have decayed.
Why can’t we make a ratio and predict
when all will decay???
Answer
 The concept of half-life relies on a lot of
radioactive atoms being present. As an example,
imagine you could see inside a bag of popcorn as
you heat it inside your microwave oven. While
you could not predict when (or if) a particular
kernel would "pop," you would observe that after
2-3 minutes, all the kernels that were going to
pop had in fact done so. In a similar way, we
know that, when dealing with a lot of radioactive
atoms, we can accurately predict when one-half
of them have decayed, even if we do not know
the exact time that a particular atom will do so.
HALF-LIFE
 Range fractions of a second to billions of
years.
 Is a measure of how stable the nuclei is.
 No operation or process of any kind (i.e.,
chemical or physical) has ever been
shown to change the rate at which a
radionuclide decays.
How to calculate half-life?
 The half life of first order reaction is a
constant, independent of the initial
concentration.
 The decay constant and half-life has the
relationship :
 hl = ln(2) / λ
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Calculations for half-life
 As an example, Technetium-99 has a
half-life of 6 hours.This means that, if
there is 100 grams of Technetium is
present initially, after six hours, only 50
grams of it would be left.After another 6
hours, 25 grams, one quarter of the initial
amount will be left. And that goes on like
this.
25
Bye!
26
Calculating Half-Life
 R (original amount)
 n (number of half-lifes)
R . (1/2)n
Try it!!!
 Now lets try to solve a half-life calculation
problem…
 64 grams of Serenium-87, is left 4 grams
after 20 days by radioactive decay. How
long is its half life?
Solution
 Initially, Sr is 64 grams, and after 20
days, it becomes 4 grams.The arrows
represent the half-life.
64 g 1/2
64 . ½ 1/2
64 . ½ . ½ …
It goes like this till it reaches 4 grams, in 20
days.
30
Solution
 We have to find after how many
multiplications by ½ does 64 becomes 4.
 We can simply state that,
64 . (1/2)n
Where n is the number of half lifes it has
experienced.
Solution
64 .
6-n
2
n
(1/2)
=
=4
2
2
n = 4 half-lifes
And as we are given the information that this
process happened in 20 days ;
4 half-lifes = 20 days
1 half life = 5 days
Tataa!!! We have found it really easily!
Questions
 Explain the reason for why can’t we predict
when/if a nucleus of a radioactive isotope with
a known- half life would decay?
 Define half-life briefly.
Questions
 Explain the law of conservation of
nucleon number.
 Does nuclei decay all at once/ how does
it decay?
 A quantity is said to be subject to
exponentional decay if…?
THE END!!!
 Resources:
 http://cathylaw.com/images/halflifebar.jpg
 http://burro.astr.cwru.edu/Academics/Astr221/HW/
HW3/noft.gif
 http://www.chem.ox.ac.uk/vrchemistry/Conservatio
n/page35.htm
 www.gcse.com/ radio/halflife3.htm
 www.nucmed.buffalo.edu/.../ sld003.htm
 http://www.iem-inc.com/prhlfr.html
 http://www.math.duke.edu/education/ccp/materials/
diffcalc/raddec/raddec1.html
 http://www.mrgale.com/onlhlp/nucpart/halflife.htm