half life

							        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.



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    Exponentional Decay

      A quantity is said to be subject to
       exponentional decay if it decreases at a
       rate proportional to its value.




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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


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     Relating it to radioactive
     decay law:
      Here comes our first equation AGAIN, try
       to look it with the new perspective:
      ∆N = - λN
       ∆t




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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.

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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.



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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)




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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.


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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
25
     this.
     Bye!




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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.
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              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 .      (1/2)n     =4
   2 6-n   =   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