Range of alpha particles in a silicon detector

[neural_jam]

Hi,
I'm trying to find the range of α-particles in silicon; I can work out the stopping power, \frac{dE}{dx}, but the reference I'm using then states that I need to integrate it as follows:

R=\int_T^0 (-\frac{dE}{dx} ) ^{-1} dE

The thing is, I'm not sure as to how to even start this integration, can anyone help?

I can actually look up the value using the page below to calculate it, but I'd like to check it by doing it myself.

http://physics.nist.gov/PhysRefData/Star/Text/ASTAR.html

Also this page gives the units of range in g/cm², can anyone explain why it's this and not just cm or m? I've seen in other places where g/cm² and cm seem to be interchangeable, so if it gives the range as 7.375x 10^-03g/cm², can I just use it as 7.375x 10^-03cm?

Many thanks!

 

[deccard]

Hi,
The thing is, I'm not sure as to how to even start this integration, can anyone help?

Also this page gives the units of range in g/cm², can anyone explain why it's this and not just cm or m? I've seen in other places where g/cm² and cm seem to be interchangeable, so if it gives the range as 7.375x 10^-03g/cm², can I just use it as 7.375x 10^-03cm?

Try to do the integration by assuming a constant stopping power. The stopping power is different for different alpha energies, but gives at least an estimation of the range. What is the kinetic energy of your alpha particle?

You of course cannot make g/cm² to cm just by changing the unit. What happens if you multiply this by the density of silicon?

 

[neural_jam]

You of course cannot make g/cm² to cm just by changing the unit. What happens if you multiply this by the density of silicon?

Did you mean divide it by the density of Si? If so you get cm, which is very useful, thankyou.

However, I don't quite understand what I'm doing when I do this; I mean how do they get to the g/cm² units in the first place? Also, why do they use this unit for range instead of cm or m or whatever?

Many thanks

 

[deccard]

Did you mean divide it by the density of Si? If so you get cm, which is very useful, thankyou.

However, I don't quite understand what I'm doing when I do this; I mean how do they get to the g/cm² units in the first place? Also, why do they use this unit for range instead of cm or m or whatever?

*Ahem*, Yes I mean divide. Thicknesses are many times given in g/cm² for for example beam target's. This is because the absorption of radiation in a target is dependent on the mass in the target.

2 cm gaseous nitrogen target is very different from 2 cm lead target. Instead of saying that you have 2 cm nitrogen target with density of 1.03mg/cm³ and 2 cm lead target with density of 11.3g/cm³, you could just say that you have targets with thicknesses 2.06mg/cm² and 22.6g/cm² without actually mentioning the target material and people already have an idea how radiation is absorbed in the target.

What a about the integration did you get it?