How can I determine the absorption coefficient \mu?

[Kahsi]

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

$$I = I_0e^{-x\mu}$$

How can I find out the value of $$\mu$$ 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.

 

[Kahsi]

I have done this,

$$I = I_0e^{-x\mu}$$
$$\frac{I}{I_0} =e^{-x\mu}$$
$$\ln\left(\frac{I}{I_0}\right) =-x\mu$$
$$\ln\left I =-x\mu + \ln I_0$$

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

$$a = \mu = y'$$

then I just have to do a linear regression and get the value of $$\mu$$.

Then $$\mu = 0,205$$. Does this seem correct?

 

[OlderDan]

I have done this,

$$I = I_0e^{-x\mu}$$
$$\frac{I}{I_0} =e^{-x\mu}$$
$$\ln\left(\frac{I}{I_0}\right) =-x\mu$$
$$\ln\left I =-x\mu + \ln I_0$$

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

$$a = \mu = y'$$

then I just have to do a linear regression and get the value of $$\mu$$.

Then $$\mu = 0,205$$. Does this seem correct?

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