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!!!! ∆N = - λN ∆ t Now, here is our little old equation: POF!!! ∆N = - λN ∆ 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 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

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 64 . ½ 64 . ½ . ½ … It goes like this till it reaches 4 grams, in 20 days. 1/2 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 . (1/2)n = 4 26-n = 22 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/Conservation/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