# Determine the thickness of aluminium using γ-rays

• garyd

## Homework Statement

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Hi all,
I have been given a mini-project to complete which involves a block of aluminium which is stuck to a piece of wood and taped so that where the aluminium and wood touch is unknown. I have been told that I need to design an experiment to measure the thickness of the aluminum using γ-rays.

Firstly I have to determine the linear absorption coefficient (μ) for the aluminium and wood and then use the information to determine the aluminium thickness without the use of any other instrumentation.

## Homework Equations

R=R(0)*e^(-μx) (1)

lnR=lnR(0)-μx (2)

where R=counting rate, R(0)= value for no absorber and x=thickness

## The Attempt at a Solution

Taking the natural log of both sides in equation (1) leaves equation 2, which is
the equation of a line i.e. y=mx+c ( would like confirmation this is correct )

The experiment I am considering involves the use of a Geiger-Muller tube and counter. I will have a source, maybe americium-241, placed at a point and take a number of counts with no aluminium in the path to the G-M tube and get the average count R (0). I will then get 4 blocks (10mm,20mm,30mm &40mm) of aluminium of which the thickness is known. Take readings with each block and obtain average counts (R). I will then plot the ln(R) as a function of thickness (x).
If my thinking is correct the linear absorption coefficient (μ) should be the slope of the line. I will repeat the procedure for the wooden blocks.

Once I have μ I should then be able to repeat the procedure with the unknown blocks and solve equation (1) for x.

One thing I cannot figure out is how to calculate the thickness with the wood stuck to the aluminum. Can it be done without taking them apart?
Also much emphasis has been put on calculating the uncertainty of the experiment. I was wondering what is the correct way to estimate the uncertainty of the counts of a G-m tube?

If someone could tell me if I am heading in the right direction to solve the problem and also would like some direction on the calculation of the uncertainties.

Thanks for taking the time to read my post, any help would be much appreciated.

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One thing I cannot figure out is how to calculate the thickness with the wood stuck to the aluminum. Can it be done without taking them apart?
You will need the total thickness of the object. And you have to consider both in the calculation.

Also much emphasis has been put on calculating the uncertainty of the experiment. I was wondering what is the correct way to estimate the uncertainty of the counts of a G-m tube?
The counts follow a Poisson distribution - for many counts, this is approximately a Gaussian distribution.

If someone could tell me if I am heading in the right direction to solve the problem and also would like some direction on the calculation of the uncertainties.
Looks good so far.

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