Solid plastic scintillator, Pilot B

[_Andreas]

Homework Statement

Calculate the energy loss $$\Delta$$T of protons, deuterons and $$\alpha$$'s between 10 and 200 MeV in passing through a 2-mm thickness of solid plastic scintillator (the name of the plastic seems to be Pilot B).

Homework Equations

The stopping power equation, which is too long for me to write here, though.

The Attempt at a Solution

$$\Delta$$T should be (dT/dx)*thickness of scintillator. My main problem, however, is with the scintillator. I have been given it's density (1,03 g/cm^3), but the stopping power requires me to have it's different Z and A values as well as its I values. The obvious problem is to know what the constituents of this plastic are, and how many of each sort of them there are in a "plastic molecule" of this kind. I'm lost!

 

[Jhero]

Hello,

Thank you for your question. In order to calculate the energy loss of protons, deuterons, and alpha particles passing through a 2-mm thickness of solid plastic scintillator, we will need to first determine the composition of the plastic.

After some research, I have found that Pilot B is a type of plastic scintillator known as Polyvinyltoluene (PVT). This plastic is composed of carbon and hydrogen atoms, with a molecular formula of (C9H10)n.

In order to calculate the energy loss, we will need to use the stopping power equation, which is given by:

dE/dx = -K * Z/A * (Z/A + 1) * ln(I/2mV^2)

Where dE/dx is the energy loss per unit distance, K is a constant, Z/A is the atomic number to atomic mass ratio of the material, I is the mean excitation energy, and m and V are the mass and velocity of the particle, respectively.

Since we know the density of PVT (1.03 g/cm^3), we can determine the number of moles of PVT in a 2-mm thickness of the material. From there, we can use the molecular formula to determine the number of carbon and hydrogen atoms in the sample.

Using the atomic and molecular weights of carbon and hydrogen, we can then calculate the Z/A ratio for PVT. The mean excitation energy for this material is approximately 60 eV, which can be found in tables or calculated using the Bethe-Bloch equation.

Once we have all of these values, we can plug them into the stopping power equation and calculate the energy loss for protons, deuterons, and alpha particles passing through the 2-mm thickness of PVT.

I hope this helps. Let me know if you have any further questions or need any additional clarification.