The Mystery of Half- Life and Rate of Decay

The Mystery ofHalf- 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

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: 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 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! • . (1/2)n = 4 26-n = 22

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

The Mystery of Half- Life and Rate of Decay