Calculating pressure / energy difference confusion

In summary, the conversation discusses the determination of electron density in a gas layer and the calculations involved in creating a theoretical curve for a Bragg plot. The equations used include the energy loss equation, the energy and pressure difference equations, and the equivalent form of the energy loss equation. The goal is to plot the energy and differential energy loss as a function of pressure, and the speaker is struggling to understand the instructions and complete the task.
  • #1
Farang
18
7

Homework Statement



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

Homework Equations


All above...

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?
 
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  • #2
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...
 

1. What is the difference between pressure and energy?

Pressure is a measure of force per unit area, while energy is the ability to do work or cause change. Pressure can be thought of as a force distributed over a certain area, while energy is the capacity for a physical system to do work.

2. How do you calculate pressure?

Pressure can be calculated by dividing the force acting on an object by the area over which the force is applied. The formula for pressure is P = F/A, where P is pressure, F is force, and A is area.

3. What are some common units for pressure and energy?

Some common units for pressure include pascals (Pa), atmospheres (atm), and pounds per square inch (psi). Energy can be measured in joules (J), calories (cal), or electron volts (eV).

4. How can pressure and energy be related?

Pressure and energy can be related in various ways, depending on the system being studied. For example, in a gas, pressure and energy are related by the ideal gas law, which states that pressure is directly proportional to the temperature and number of moles of gas, and inversely proportional to the volume.

5. What are some real-world applications of calculating pressure and energy?

Calculating pressure and energy is important in many scientific and engineering fields. Some examples include designing efficient engines for cars and airplanes, understanding fluid dynamics in weather patterns, and determining safe diving depths for scuba divers.

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