# half-life

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### The Mystery of Half- Life and Rate of Decay:

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

### Before we start....:

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....:

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...:

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 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:

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

### PowerPoint Presentation:

... 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:

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:

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 = - λ N ∆ t

### Relating it to radioactive decay law::

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

### PowerPoint Presentation:

Here comes our first equation AGAIN, try to look it with the new perspective: ∆N = - λ N ∆ t Relating it to radioactive decay law: 11

### What was that?!!!:

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...:

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...:

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!!!! :

Got it!!!! Now, here is our little old equation: ∆N = - λ N ∆ t POF!!! Now it has become the radioactive decay law! (yehu)

### What was that???:

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?:

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…:

As seen in the figure below… Please just focus on how it decays exponetionally. Half-life will be discussed soon…

### HALF-LIFE:

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!!!:

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:

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:

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?:

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:

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:

Calculating Half-Life R (original amount) n (number of half-lifes) R . (1/2) n

### Try it!!!:

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:

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:

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:

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 2 6-n = 2 2

### Questions:

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:

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!!!:

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 