The Mystery of Half- Life and Rate of Decay The truth is out there... BY CANSU TÜRKAY 10-N

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

... 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. Radioactive Decay Law and its Proof 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

 Here comes our first equation AGAIN, try to look it with the new perspective:  ∆N = - λN ∆ t Relating it to radioactive decay law: 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 ∆ t POF!!!  Now it has become the radioactive decay law! (yehu)

What was that???  N 0 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 24

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

26 Bye!

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 64. ½64. ½. ½ … It goes like this till it reaches 4 grams, in 20 days. 1/2 30

Solution  We have to find after how many multiplications by ½ does 64 becomes 4.  We can simply state that, Where n is the number of half lifes it has experienced. 64. (1/2) n

Solution 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! 64. (1/2) n = n = 2 2

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:   HW3/noft.gif HW3/noft.gif HW3/noft.gif  n/page35.htm n/page35.htm n/page35.htm  radio/halflife3.htm radio/halflife3.htm radio/halflife3.htm  sld003.htm sld003.htm sld003.htm   diffcalc/raddec/raddec1.html diffcalc/raddec/raddec1.html diffcalc/raddec/raddec1.html 