How can I determine the absorption coefficient \mu?

In summary, the conversation involves a lab experiment with a GM-detector and leadboards to measure decay. The equation I = I_0e^{-x\mu} is used to find the value of the linear absorption coefficient \mu, and a linear regression can be used to calculate it. The final value obtained for \mu is 0.205, with a negative slope indicating a positive value for \mu.
  • #1
Kahsi
41
0
Hi.

I have done this lab where I had a GM-detector and some leadboards. I was mesuring how many decay it detected and tryed 0 - 6 leadboards to see the difference.

We know that

[tex]I = I_0e^{-x\mu}[/tex]

How can I find out the value of [tex]\mu[/tex] in the http://home.tiscali.se/21355861/bilder/absorption.GIF (the linear absorption coefficient)?

I = number of decays?

I just need some hints.

Thank you.
 
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  • #2
I have done this,

[tex]I = I_0e^{-x\mu}[/tex]
[tex]\frac{I}{I_0} =e^{-x\mu}[/tex]
[tex]\ln\left(\frac{I}{I_0}\right) =-x\mu[/tex]
[tex]\ln\left I =-x\mu + \ln I_0[/tex]

Then if we take ln(numbers of decays) we would have this graph:
y = ax + b

[tex]a = \mu = y'[/tex]

then I just have to do a linear regression and get the value of [tex]\mu[/tex].

Then [tex]\mu = 0,205[/tex]. Does this seem correct?
 
Last edited:
  • #3
Kahsi said:
I have done this,

[tex]I = I_0e^{-x\mu}[/tex]
[tex]\frac{I}{I_0} =e^{-x\mu}[/tex]
[tex]\ln\left(\frac{I}{I_0}\right) =-x\mu[/tex]
[tex]\ln\left I =-x\mu + \ln I_0[/tex]

Then if we take ln(numbers of decays) we would have this graph:
y = ax + b

[tex]a = \mu = y'[/tex]

then I just have to do a linear regression and get the value of [tex]\mu[/tex].

Then [tex]\mu = 0,205[/tex]. Does this seem correct?

Except for dropping a minus sign when relating your slope parameter (a) to [itex]\mu[/itex], everything looks good. Your graph should be linear with negative slope giving you a positive value for [itex]\mu[/itex].
 

Related to How can I determine the absorption coefficient \mu?

1. What is an absorption coefficient?

An absorption coefficient is a measure of the amount of light or other electromagnetic radiation that is absorbed by a material when it passes through it. It is expressed as a decimal or percentage value and can vary depending on the type of material and the wavelength of the radiation.

2. How is the absorption coefficient calculated?

The absorption coefficient is calculated by measuring the intensity of light or radiation passing through a material before and after it passes through the material. The difference in intensity is then used to determine the amount of absorption that occurred, which is expressed as a coefficient value.

3. What factors can affect the absorption coefficient?

The absorption coefficient can be affected by various factors such as the type of material, its thickness, the wavelength of the radiation, and the temperature. Different materials have different absorption coefficients, and the coefficient can also change depending on the wavelength of the radiation passing through it.

4. What is the significance of the absorption coefficient in scientific research?

The absorption coefficient is an important parameter in scientific research, particularly in the fields of optics and spectroscopy. It can provide valuable information about the properties of a material and how it interacts with light or other electromagnetic radiation. It is also used to determine the concentration of a substance in a solution through a process called absorbance spectroscopy.

5. Can the absorption coefficient be used to compare different materials?

Yes, the absorption coefficient can be used to compare different materials as it provides a measure of how much light or radiation is absorbed by each material. This can be useful in determining which material is more suitable for a particular application, such as in the development of solar panels or optical devices.

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