[whotosee]

An X-ray beam of initial intensity 50 Wm−2 is incident on soft tissue of attenuation coefficient 1.2 cm−1. Calculate its intensity after it has passed through a 5.0cm thickness of tissue.

A hint for this question is:
The attenuation coefficient is given in cm-1, hence you can leave the thickness in cm.

So according the hint I get the answer:
I=Ioe^(-ux)
50 x e^(-1.2x5)= 0.12Wm-2, which is the correct answer according to the textbook.

But why should I leave the attenuation coefficient and the thickness in cm, when the intensity is measured in Wm-2? I thought that the calculation should have been:
50 x e^(-0.0125x0.05)= 49.97Wm-2

Confused, please help

[Stonebridge]

(Original post by whotosee)
An X-ray beam of initial intensity 50 Wm−2 is incident on soft tissue of attenuation coefficient 1.2 cm−1. Calculate its intensity after it has passed through a 5.0cm thickness of tissue.

A hint for this question is:
The attenuation coefficient is given in cm-1, hence you can leave the thickness in cm.

So according the hint I get the answer:
I=Ioe^(-ux)
50 x e^(-1.2x5)= 0.12Wm-2, which is the correct answer according to the textbook.

But why should I leave the attenuation coefficient and the thickness in cm, when the intensity is measured in Wm-2? I thought that the calculation should have been:
50 x e^(-0.0125x0.05)= 49.97Wm-2

Confused, please help

It seems odd but it's ok.
The units on the LHS are Wm^-2 and the units on the RHS are Wm^-2 x e^(number)
e^(number) has no units (it's a pure number) so it doesn't affect the units of that side of the equation. The number in the bracket is also a pure number because its units cancel out.
cm.cm^-1 gives no unit.
So as long as the coefficient and the length are in the same length unit it works!

[whotosee]

(Original post by Stonebridge)
It seems odd but it's ok.
The units on the LHS are Wm^-2 and the units on the RHS are Wm^-2 x e^(number)
e^(number) has no units (it's a pure number) so it doesn't affect the units of that side of the equation. The number in the bracket is also a pure number because its units cancel out.
cm.cm^-1 gives no unit.
So as long as the coefficient and the length are in the same length unit it works!

Thank you, the units cancelling out makes sense, but it means that I'll get a different answer every time I use a different unit?
(Like when I got 49.97Wm-2 when I converted everything to metres instead of 0.12Wm-2 when using cms)
In that case what units am I supposed to be using? Thanks

[Stonebridge]

(Original post by whotosee)
Thank you, the units cancelling out makes sense, but it means that I'll get a different answer every time I use a different unit?
(Like when I got 49.97Wm-2 when I converted everything to metres instead of 0.12Wm-2 when using cms)
In that case what units am I supposed to be using? Thanks

You correctly converted cm to m
5cm = 0.05m
You divide by 100
But you don't do this when you convert cm^-1 to m^-1
Then you multiply by 100

For example, if you have 5 items in a line per cm, then you would have 500 in a line 1m long. That is 500 per m

[whotosee]

(Original post by Stonebridge)
You correctly converted cm to m
5cm = 0.05m
You divide by 100
But you don't do this when you convert cm^-1 to m^-1
Then you multiply by 100

For example, if you have 5 items in a line per cm, then you would have 500 in a line 1m long. That is 500 per m

Aah, I see!! Thank you very much