# Lab Report Example: Modeling Radioactive Decay

Date:  2021-04-06 09:31:08
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Vanderbilt University
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Radioactive is the process whereby the unstable atomic nucleus of a substance spontaneously breakdown thus losing its energy by releasing or emitting radiation such as gamma-ray, beta particles, alpha particles or electrons. Radioactive decay is the process of determining how to hold an organism is, it is a random process, and it is highly accurately incorrect to tell when an atom will undergo decay. Three decaying processes were the first to be discovered, and they are beta decay, alpha decay and gamma decay. Where radioactive occurs, there is transmutation (this is the change of one element to another element due to the impact of changes within the nucleus).

Radioactive randomly emits electors, protons, and radiation and through this process, they undergo transformation to a new substance. For instance, we use an amount of radioactive substance, and we label it N it is noted that the time rate t of change taken by the substance its proportional to the absolute negative amount of the material.

The following equation is used when modeling a radioactive decay of materials (atoms):

N(t) = N0 e-lt

In this case, the symbol represents:

N(t): this is the amount of the decaying material that is remaining after the time t.

T: time taken

l: the constant of the radioactive decay

N0: this is the initial amount of the element.

Taking into consideration carbon-14 using the same formula, it has a half-life of 5730 years. It means that at exactly after 5730 years passing by, half of the carbon-14 initial will have undergone decay. Using the information we can be able to calculate and solve the constant decay l of carbon-14.

Time taken t for decaying of carbon-14 = 5730

Half-life= 0.5

N(5730) = 0.5N0 = N0 e-lt

Henceforth:

e-lt= 0.5 if we have the natural log of both sides it is easy to solve the equation by re-arranging.

l = ln(1/2) / -5730

l =0.000121

This is how matters which are involved with carbon-14 such as the popular carbon dating are used to determine the age of things.

Example

Remains of an organism when they are measured contain 14% of the original amount of substance of carbon-14.having in mind that carbon-14 has a half-life of 5730 years. Calculate how old the paper is.

Solution

Amount N of carbon-14 will only undergo decay after the specimen dies.

Using the equation below that was extracted:

N(t) = N0 e-0.000121t

N(t)/N0 = e-0.000121t

0.14= e-0.000121t

t = ln(0.14)/(-0.000121)

t= 16,253

its evident the organism had died 16,253 years ago.

Also a similar question but with a different approach.

N(t)= N02-t/ l, whereby l= 5730

The remains are containing on 14% of the original specimen at time t.

N(t)/N0 = 14/100 = 2-t/ l

-t/ l = log2(14/100) =

t = llog2(100/14)

t= 16,253 years.

Experiment 1: modeling a radioactive decay using a set of dices.

It is not possible to tell when particular radioactive nuclei will undergo decay but it is possible to determine with a great length of probability the rate of decay for a mass of nuclei in a given sample. This is made possible since for a single type of a radioactive isotope the rate of decay remains to be constant.As discussed earlier the decay of a radioisotope is a process which is random since it is not influenced by the environment or its actual history.

Apparatus

80 dice in a plastic bag

A plastic cup

A data packet.

Procedure

Pour out all the 80 dice into the plastic bag.

Shake the cup filled with dice.

Roll out all the dice onto a table. (Each roll of the dice simulates one minute).

Take out all the dice that were to land with the given unknown number face up. Place them aside.

Note down the number of dices that is remaining on the datasheet.

Put the dice which is remaining back to the plastic cup.

Repeat the procedure sometimes as you fill the datasheet.

Average the figures that are heading across at each time as you record.

Plot a graph of min vs. counts/min

Time (min) Run 1 Counts/min Run 2 Counts/min Run 3 Counts/min average

0 1 80 80 80 80

2 69 62 71 67.3

3 37 34 45 38.7

4 34 26 33 31

5 30 23 23 25.3

6 19 17 13 16.3

Calculate the values that are based on the average run. (Theoretical half-life = 3.80min).

A graph of min against counts/min.

Having such a graph it is easier to find by calculating the constant which makes the area under the curve equal to 1.

The rate of decay of a substance is usually the same as the number of atoms which decay or are emitted after every second. The rate at which a radioactive substance undergoes decay will depend on the number of the atoms that have not decayed. The half-life is the time that is taken for half the number of atoms in a given radioactive material to undergo decay. As discussed earlier radioactive decay is not affected by any environmental factors such as pressure, temperature or atmospheric pressure.

Experiment 2: Modelling Radioactivity decay using pennies

Objective

To discover the number of pennies that are remaining after you shake, pour and select for heads changes after every shake. After collecting the data and drawing the graph compare the graph of the pennies to that of the radioactive decay.

Apparatus

Two large containers with covers

100 pennies

Datasheet

Procedure

Place the given 100 pennies in one of the large covered containers. Take the bottle and shake it for several times and remove its cover. With a lot of care empty the container on a table and ensure that the pennies do not roll away.

All the coins that have their head side turned upwards should be removed and placed in the second container. On your given data sheet note down the numbers of pennies that have been removed and also the ones that are remaining.

Those remaining pennies that have their tails showing should be placed back to the container shake the bottle again randomly and put the pennies on the table or any flat surface available. Sort out the pennies exactly like procedure number III and record the data,

The process is repeated as many times as possible until no penny is left on the container.

When through return all the pennies to their original container and clean up your station.

Questions to examine the data.

How many shakes were counted before the pennies number remaining was showing half of the original number of pennies? How make shakes count showed one-fourth of the pennies remaining? According to the experiment done what is the possible half-life of the pennies about the number of shakes?

It's evident- that the final graph will be much closer to that of carbon-14 most especially the curve. Through this experiment we are able to put into test a hypothesis through inference, there is a connection between the pennies and the radioactive research elements samples. The scientists can determine the age of organism by looking what percentage of radioactive material is present in the given organism.

This is how carbon-14 is used to date materials which are as old as even 60,000 years old. All living things are made of organic matter that is why we can live and exist; the organic matter contains some form of carbon. When any organism dies, the carbon contained in the organism cannot be replaced and continues to stay within the organism until the decomposition process takes place that is when it gets back to the ecosystem.

When radioactive decaying takes place, there is no effect on the environment, but a series of conservation apply. Some of the conservations are:

Preservation of the charge

Conservation of momentum

Conservation of energy

Maintenance of the number of nucleons

When radioactive is used to determine how old material is it is referred to as carbon dating. The use of carbon-14 delivers the method this is due to the existence of carbon 14 in each and every living organism. To calculate the age of something, you record the activity of carbon-14 and have a comparison to what you would have expected by adding the numbers to the decay equation and considering the half-life.

The following are characteristics of radioactive emissions.

Characteristic Alpha particle Beta particle Gamma ray

Nature Positively charged helium nucleus, He Negatively charged electron, e Neutral

Electric field Bends to the negative plate Turns to the positive plate Does not bend, it is neutral.

Magnetic field Bends a little showing that it has a big mass. The direction of the bend indicates that it is positively charged. Bends a lot showing that it has a small mass. The direction of the bend indicates that it is negatively charged. Does not bend, it is neutral.

Ionising power Strongest Intermediate Weakest

Penetrating power low Intermediate High

Stopped by A thin sheet of paper A few millimetres of aluminium A few centimetres of lead or concrete

Range in air A few centimetres A few metres A few hundred metres

Speed 1/20 X the speed of light, c 3%-99% of the speed of light, c The speed of light, c

REFERENCES

Bakac, M., Tasoglu, A. K., & Uyumaz, G. (2011). Modeling radioactive decay. Procedia-Social and Behavioral Sciences, 15, 2196-2200.

Cappellaro, E., Mazzali, P. A., Benetti, S., Danziger, I. J., Turatto, M., Della Valle, M., & Patat, F. (2007). SNIa light curves and radioactive decay. arXiv preprint astro-ph/9707016.

Nelson, A. W., Eitrheim, E. S., Knight, A. W., May, D., Mehrhoff, M. A., Shannon, R., ... & Schultz, M. K. (2015). Understanding the radioactive ingrowth and decay of naturally occurring radioactive materials in the environment: an analysis of produced fluids from the Marcellus Shale. Environmental Health Perspectives (Online), 123(7), 689.

Segre, E. (2013). Nuclei and particles: an introduction to nuclear and subnuclear physics, (dover books on physics). Dover Publ..

Thorek, D. L., Ogirala, A., Beattie, B. J., & Grimm, J. (2013). Quantitative imaging of disease signatures through radioactive decay signal conversion. Nature medicine, 19(10), 1345-1350.]  #### Request Removal

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