# Calculating pressure / energy difference confusion

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1. Feb 18, 2017

### Farang

1. The problem statement, all variables and given/known data

The electron density per area, $N$ for a gas layer of thickness 10 cm can be determined
$$n = k \times p \times 2.47 \times 10^{19}$$
For each adjacent sets of pressure data using Matlab, calculate the average energy in keV, the pressure difference in hPa, the energy difference in keV and then evaluate $-\frac{\Delta E}{\Delta p}$ in keV/hPa. Plot this as a function of the average energy, along with the theoretical energy loss, that can be calculated using analysis based on equation
$$-\frac{dE}{dx}=\frac{4\pi n Z^{2}}{m_{e}v^{2}} \left ( \frac{e^{2}}{4 \pi \epsilon_{0}} \right )^{2} ln\left ( \frac{2m_{e}v^{2}}{I} \right )$$
Using $\mu = \frac{m_{e}}{m_{He}} = \frac{511 keV}{3.727 GeV} = 1.371 \times 10^{-4}$ and $Z = 2$.
$$-\frac{dE}{dx}=\frac{2\pi Z^{2}}{\mu E} \frac{N(p)}{p} \left ( \frac{e^{2}}{4 \pi \epsilon_{0}^{2}} \right )^{2} ln\left ( \mu \frac{4E}{I} \right )$$
$$-\frac{dE}{dp}=\frac{k}{E} \times 2.41\times10^{-29} \frac{J^{2}}{hPa} \times ln\left ( 5.848\times10^{-4} \frac{E}{I} \right )$$
which can be written in an equivalent form
$$-\frac{dE}{dp}=\frac{k}{E} \times 940 \frac{keV^{2}}{hPa} \times ln\left ( 5.848\times10^{-4} \frac{E}{I} \right )$$
which is suitable for the creation of a theoretical curve that can be compared to the experimental data by plotting them on the same axes.

You need to present your data in the form of a Bragg plot, which shows both
the energy and differential energy loss as a function of pressure, as shown by the exemplar data in figure 3.2

2. Relevant equations
All above...

3. The attempt at a solution

Following the lab script has always been the most difficult part of the course for me for some reason. Often I can't figure out what is that I am supposed to do or even what I've just done. Perhaps someone here will be able to make sense of this...

So far I have 2 tables(one for Helium and one for air) with 4 rows each(Max # of impulses, Energy(keV), Average energy(keV) and Pressure(mbar)).

How / why / between what pressure difference does it want me to calculate?

2. Feb 18, 2017

### Farang

Ok I think I'm getting there, painfully slowly... I need to plot alpha energy and energy loss as a function of pressure. What a way to spend a Saturday night...