Exploring the Realm of X-rays: Spectroscopy and Diffraction

Introduction

A German physicist who went by the name of Conrad Rontgen discovered x-rays in the year 1895. X-rays are of a similar nature to light, since they both make up part of the electromagnetic spectrum. X-rays however have short wavelength whereas light has longer wavelength. These electromagnetic waves are made by taking an electron or particle that is electrically charged and clashing it with a metal target. X-rays are used in different fields of science and technology, and over time it has become a ”tool” that has revolutionized the way we saw the world.

In this report I will delve into the realm of spectroscopy and diffraction to understand how x-rays are intergrated into science. I will cover a brief history on the topic, as well as its impact in our modern day era.

Theoretical Outline

The word ”spectroscopy” is a very common term in science, and it spans across all fields of science. Its roots can be dated back to the early 1700s during the time of Sir Isaac Newton.

Get quality help now

RhizMan

Verified writer

Proficient in: Physics

4.9 (247)

“ Rhizman is absolutely amazing at what he does . I highly recommend him if you need an assignment done ”

+84 relevant experts are online

Hire writer

He made use of a prism to shine visible light through it. What he observed was that the light emerged from the prism in a dispersed manner. Spectroscopy is a branch of science that deals with analysis of the absorption and emission of light and other radiation by matter. There are several different spectroscopic techniques used, different regions of the electromagnetic spectrum make use of different spectroscopic techniques. With the x-ray region it is x-ray spectroscopy and with the gamma ray regions it is gamma ray spectroscopy.

The main topic of this lab report is about x-rays, so we focus on x-ray spectroscopy as well as x-ray diffraction. Spectroscopy as mentioned above is a technique used to study the interaction between electromagnetic waves and matter, in our case the EM wave would be x-rays. With x-ray diffraction, we look into how x-rays are scattered about by the atoms in the object. So when x-rays are incident on any type of matter, it interacts with the particles of that matter. From these interactions, some of the x-rays are absorbed by the particles, and some are transmitted.

Shown above is what is known as a characteristic x-ray diagram. It shows two sharp peaks, which are produced in the K-shell of any given atom. When fast moving electrons are bombarded onto a metal target, the electrons are removed from the inner shell. From these constant bombardments, the removed electrons are replaced by electrons that are in a different energy state, i.e transition of electrons. So x-rays that are produced from transitions from n=2 to n=1 are referred to as K-alpha x-rays, and for transitions from n=3 to n=1, these transitions are called K-beta x-rays.

The word ”Bremastalling” means breaking radiation and it is a basic representation to show the radi- ation that is given off after electrons have been slowed down. It is represented by a continuous energy distribution, and depending on the energy of the fast moving electrons the relative intensity rises with an increase in energy.

So how does x-ray spectroscopy actually work? If we have an atoms that is at an unstable state its electrons change energy levels from which we refer to as transitioning. A similar scenario would be when a particle or atom is constantly colliding with particles that have lots of kinetic energy. This when x-ray spectroscopy comes into play, we make use of it to calculate or measure the energy changes between the different transition states. This way we can have a clearer understanding on how different materials interact.

As we may know by know x-ray spectroscopy has a range of applications that it can be used on. For instance with anthropologists and archaeologists, they can make use of this technique in discovering information about ancient artifacts. Even astrophysicists use x-ray spectroscopy to learn about how objects in outer space work. Furthermore, it is used in the medical field in CT scan machines.

In x-ray diffraction there is a method used to analyse the crystalline structure of matter. W.L Bragg simplified how we understand the ways in which beams are diffracted in a crystal. Using x-ray diffraction method, we can learn more about the crystallinity of a fiber. We can learn amongst others things the internal structure, shape and spacing between particles.

In our modern day time x-ray diffraction has been used countless times because it uses the x-rays dual particle nature in getting information from crystalline objects. As mentioned above, Bragg’s law is used to describe the diffraction of x-rays. Bragg’s law, given by:

nλ = 2dsinθ

The above law simply states that when an x-ray is incident on a crystal surface, the angle at which the ray is incident on the crystal is the same as the angle at which it is reflected. With ’d’ being the path difference, ’n’ a positive integer value and ’lambda’ the wavelength.

Aims

From this experiment our main objectives are as follows:

1. Finding what Planks constant value is.
2. To determine what kind of impact nickel filter.
3. Identifying what the unknown filter is.
4. And obtaining the x-ray spectrum from the results we ’obtained’.
5. Finding the Crystal structure of copper powder.

Apparatus used

1. Copper
2. Computer
3. X-ray generator

Experimental Proceedure

The experiment was actually not performed due to the fact that the equipment’s weren’t working at the time. However, our demonstrator gave us a somewhat brief outline on what had to be done. So the experiment was divided into two parts, namely part A and B. Below as the experimental procedures.

Part A For the first part of the experiment, the current had to be set at 10mA and the energy at 30kV. The slit beam was then replaced with a pinhole beam focus. After that we made use a calcite crystal by mounting it onto the specimen support in the sample holder. A stainless steel was used as a shield and it was placed over the sample. To set an specific angle the goniometer of the diffractometer was used to calibrate the angle we wanted. After doing all of the required steps the computer was turned on and waited for the spectrum data to be saved. To check if the x-rays were being generated, we opened the x-ray port to see if a red beam of light was present this way we could know if the x-rays were being generated. Bragg’s law should then be used to determine the wavelengths of the peaks measured.

Part B During this part of the experiment, crystalline powders are used as a replacement for single crystals. A similar procedure is followed as above. The only difference is that the pinhole is replaced with a slit beam focus.

Calculations and analysis

x-ray spectroscopy

Our goal here is to determine Plank’s constant and to do so we should use the shortest wavelength which happens to occur at the lowest intensity. We can go about this by using the data from table 1, the following are three data points collected from the table.

Table 1: Without filter

Table 2: Unknown filter

Table 3: x-ray diffraction

·V = 25kV, 2θ = 8.40, θ = 4.20V = 30kV, 2θ = 7.57, θ = 3.79

V = 35kV, 2θ = 7.04, θ = 3.52

We can now make use of Bragg’s law to calculate the wavelength.

nλ = 2dsinθ

( × )Given that d = 3.03 10−10m The calculations below is for 35kV, the rest is tabulated in the table to come

λ = 2(3.03 × 10−10)sin(4.2) = 4.44 × 10−11m eV = (1.602 × 10−19)(30000V ) = 4.81 × 10−15 ( × ) 1 = 2.41 1010

Energy vs inverse wavelength

So from the above plot I can determine planck’s constant using the gradient which happens to be:

Using eV = hc

m = 2.0 ∗ 10−15 (in)I can determine planck’scontant.

m = hc 6.59 × 10−34m/s

After calculating planck’s constant I can use it to determine the error in percentage of what I calculated. Hence,

The next step to our analysis is to calculate the wavelengths of Kα1, Kα2 and Kβ. Using the plot below, we can determine the above wavelengths.

The table below shows the different results obtained from the plot. Next we plot a graph depicting the spectrum of an unknown filter.

Now that we have the plots for Nickel filter and spectrum with an unknown filter, the plot below represents a comparison between the different spectrum’s.

The wavelength of Kα is = 1.54A So using d = 2sinθ Therefore d = 2.10A Let K = 2a Then:

sin2θ K = k2 + h2 + l2

herefore, the table below outlines the results we obtain from doing some calculations.

Discussion

Since the experiment was actually not performed there isn’t much I can say about the accuracy of the results. The report was done by using the results given to us by our demonstrator, furthermore I used the lab manual as my instruction guide. It had all the necessary steps and information needed to complete the lab report. The experiment had two parts to it, in the first part I had to determine what the value for planck’s constant is. From the value I got for planck’s constant I compared it to the expected value. I got a percentage error of around 5.35 which is quit reasonable. In the second part, we had to study what effect nickel filter has on the radiation. What I was able to pick up was that the nickel filter reduced the radiation intensity which had an influence on the wavelength and energy.

Lastly, with regards to the lattice parameter of copper, the expected value doesn’t correlate to the expected value. It may have been due to the results we got or an error in my calculation. Nonetheless, there was a lot I learnt doing this lab report. I had better understanding of what x-rays were and its usefulness in all science related fields.

Conclusion

Our most important objective from ”conducting” this experiment was to learn more about x-ray spectroscopy and diffraction. With minimal background knowledge on spectroscopy I had some challenges understanding some concepts, but from doing extensive research I have learnt quit a lot.

Furthermore, I believe that x-ray spectroscopy has had a big influence in the field of science. We just scratched the surface, so with more time and research we can discover other ways in making good use of this technique.