Reading Quiz

Question 1:

By what mechanism were X-rays produced by Roentgen?


Roentgen observed X-rays when electrons from a cathode ray tube struck either the glass or the target within the tube.
  1. Roentgen produced X-rays through a type of radiation called bremsstrahlung. This type of radiation occurs when the atoms of a target stop and deflect incoming electrons. This deflection causes the electrons to accelerate which in turn produces electromagnetic waves. Specifically, Roentgen experimented with electrons in cathode rays hitting the glass tube of the cathode ray tube.
  2. They were discovered while working with a cathode ray tube. The x-rays were produced when the cathode rays (electrons) struck the glass tube or an object within the tube. These x-rays could pass through materials opaque to visible light and cause a fluorescent screen on the other side to fluoresce.
  3. When he was working on a cathode ray tube.
  4. While experimenting with cathode rays, he discovered rays originating from the point where the electrons impacted the glass tube or other target that passed through all materials, including those opaque to light. They strength with which they passed through decreased with increasing density.
  5. Thermionic emission produced beta waves that then collided the positive plate and emitted X-rays through secondary emission.
  6. the X-rays were produced from the point in the cathode ray tube where the electrons hit the glass tube. From this we can deduce that the electrons hitting the glass were knocking around electrons into lower energy levels this producing photons in the form of X-rays.
  7. He found that "rays" originating from the point where the cathode rays (electrons) hit the glass tube, or a target within the tube, could pass through materials opaque to light and active a fluorescent screen or photographic film.These rays are X-rays.
  8. Roentgen produced x rays using a cathode ray tube, coming from where the 'cathode' rays (electrons) hit the glass tube.

Question 2:

Explain how a crystal behaves like a 3-dimensional diffraction grating.


A diffraction grating is a set of regularly spaced slits (or obstacles). In this sense, a crystal lattice is an array of regularly spaced atoms, each acting as a scattering source, and hence, a diffraction grating in three dimensions.
  1. Diffraction patterns of X-rays indicated that X-ray wavelengths were in the order of magnitude 10^(-10)m. This is the same order of magnitude as the spacing of atoms in a crystal, thus the crystal can behave like a 3-dimensional diffraction grating for X-rays. The incoming X-rays will be scattered by different planes of atoms, thus producing a path difference between different paths of scattered light. This leads to a diffraction pattern, just as a diffraction grating would.
  2. The spacing of atoms in a crystal is of the same magnitude as the wavelength of x-rays so it acts as an effectively sized system of slits for the x-rays.
  3. The lattice structure of the array of atoms acts as a diffraction grating and filters light through in equal 3 dimensional spaces.
  4. The wavelength of x rays is on the same order of magnitude as the spacing of atoms in crystal, and since crystal is evenly spaced like a diffraction grating, it can act as such.
  5. Crystals have regularly spaced particles. This means that there are effectively very small and regular distribution
  6. W.L. Bragg explained the phenomenon as due to the scattering from various sets pf parallel planes of atoms. In a crystal, the atoms are spaced as a 3-D lattice. Waves that scatter from two successive atoms in one of these planes would be in phase, whereas that would only be the case when waves scatter from equal angles from atoms in two different planes if the distance between those two planes is some integral number of the wavelength.
  7. A 3-dimensional diffraction grating enables both constructive and destructive interference in the diffraction pattern.This would leave a series of discrete spots as reflections on the detector.In a crystal, the X-rays are diffracted by the electrons in the structure and consequently the result of an X-ray experiment is a 3-dimensional map showing the distribution of electrons in the structure.
  8. The wavelength of x rays is roughly the same as the spacing between atoms in crystals. Therefore, passing x rays through a crystal, they are deflected as though they are going through multiple slits, i.e. a diffraction grating. The reason it is 3 dimensional is obvious, because crystals are 3D

Question 3:

Identify the three features characteristic of an intensity vs wavelength (spectral distribution)
X-ray spectrum.


1. There is a continuous, varying spectrum with a minimum wavelength, peaking at some value, then dropping off to zero with increasing wavelength.
2. The minimum wavelength and overall intensity for each wavelength increased with increasing accelerating voltage for the cathode ray tube.
3. Sharp spikes appeared at particular wavelengths, and these did not change position as the intensity was altered, but did change as the target material was altered.
  1. The three characteristic feature of an intensity vs wavelength X-ray spectrum are: that the spectrum consists of a series of sharp lines called the characteristic spectrum, that there is a continuous bremsstrahlung spectrum (which is characteristic of the target material) upon which the characteristic spectrum is superposed, and that the continuous spectrum has a sharp cutoff wavelength which is independent of the target material and instead depends on the energy of the bombarding electrons.
  2. There is a cutoff wavelength below which the intensity is zero. This is independent of the material and depends only on the voltage in the x-ray tube. Corresponds to the maximum energy photon capable of being emitted given the kinetic energy of the incoming electron. The spectrum consists of sharp lines. The lines are characteristic of the material and do not appear if the cutoff wavelength was larger than the particular line. The sharp lines occur within a spectrum of continuous radiation. This was explained as resulting from the braking of electrons with various kinetic energies in the strong electric fields.
  3. 1. The spectrum consists of a series of sharp lines, called the characteristic spectrum. 2. The continuous bremsstrahlung spectrum, characteristic of the target material and varies from element to element. 3. The continuous spectrum has a sharp cutoff wavelength, independent of target material but depends on the energy of the bombarding electrons.
  4. it has sharp lines jutting out from a continuous distribution and there is a cut off wavelength where no beams are emitted
  5. 1) The spectrum consists of numerous sharp spikes, dubbed the characteristic spectrum. 2) These spikes are superimposed on the continuous bremsstrahlung, or braking radiation, spectrum, and these spikes seem to be characteristic of the target material and vary from element to element. 3) The continuous spectrum has a sharp cutoff wavelength lambda m, which is given by the formula lambda m = 1.24X10^3 / V . (V is the voltage of the x-ray tube)
  6. 1) The spectrum curves are continuous. 2) The cutoff wavelength lambda_m is independent of the target element and is related to the voltage on the x-ray tube V lambda_m=hc/eV. 3) The wavelengths of the lines are characteristics of the element.
  7. The spectral distribution of x rays has sharp 'characteristic spectrum' lines, a continuous bremstrahlung spectrum (caused by the deceleration of electrons as they aproach the electric fields of the atoms), and a sharp cutoff wavelength dependent only on the energy of incident electrons, not of the target material.

Question 4:

Describe the Compton Effect.


When X-rays strike a material, the scattered X-ray carries an energy lower than that of the incident X-ray.
  1. The Compton effect is that scattered X-rays have a higher wavelength than that of the incident X-rays. This is due to the fact that, when a photon collides with an electron, the electron absorbs some of the energy of the photon, thus leaving the photon with less energy. Therefore, according to Planck's definition of E_photon as hc/lambda, then the scattered photon would have a longer wavelength than that of the incident photon.
  2. The Compton effect refers to the change in wavelength of an photon when it collides with an electron. The electron would absorb some of the photon's energy so the outgoing photon would have a larger wavelength (less energy) than the incident photon. The change is a function of the scattering angle.
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  4. Scattered photons have less energy than incident photons as some of their energy is absorbed by the electron with which the photon collided.
  5. x rays that are diffracted are absorbed more easily.
  6. It was observed that the scattered x-rays were absorbed more readily by materials than the original, non-scattered x-ray light. Compton was the one to point out that if the scattering process were considered a "collision" between a photon of energy hf1 & momentum hf1/c, and an electron, the electron that was hit would absorb part of the incident photon's energy. The energy of the scattered photon, hf2, would have a lower frequency f2 < f1, and such the momentum would now be hf2/c. Compton then found the difference between the two wavelengths of light lambda2 - lambda1 = h/mc * (1 - cos(theta)), where theta is the scattering angle.
  7. The inelastic scattering of a photon by a charged particle, usually an electron, results in a decrease in energy and increase in wavelength of the photon is called the Compton Effect. It was observed that when X-rays of a known wavelength interact with atoms, the X-rays are scattered through an angle theta and emerge at a different wavelength related to theta.
  8. Shining x rays on electrons causes collisions between photons and electrons. These collisions must conserve momentum, and the photon is deflected (change in momentum), but the electron also changes momentum slightly. This change in momentum relates to a loss of energy of the photon, which translates to a lower frequency for the scatered (deflected) photon.

Question 5:

Describe how the Compton Effect is inconsistent with the classical perspective of light.


The classical picture of light as an electromagnetic wave striking an (effectively) free electron, assumes that the electron will begin to oscillate at the same frequency as the incident light, and thus re-radiate light at exactly the^? same frequency as the incident light.
  1. The Compton Effect is inconsistent with the classical perspective of light because, classically, the light scattered off of a substance should merely be a reflected form of the incident light. Reflection does not change the wavelength of the light, thus the incoming wavelength should be the same as the outgoing wavelength.
  2. The Compton effect considers light as a particle, not as a continuous wave.
  3. When he was working on a cathode ray tube.
  4. The bombarding of a material produced sharp lines that were a characteristic of the target element, but didn't appear if lambda m was larger than that the line. This is inconsistent with continuous radiation.
  5. the compton effect says that scattering process involves a collision between a photon and an electron. this collision is when all the energy is transferred and some is lost softening the x-rays. this is inconsistent with classical because wave energy is transferred over time and a collision with an instant transfer doesn't make sense
  6. The classical perspective of light had no problem predicting the continuous bremsstrahlung spectrum, but had a lot of trouble with the spikes, since the wavelengths of the sharp lines were a function of the target element, and the set of these spikes would always be the same fora specific target element. Furthermore, the sharp lines wouldn't even appear if the voltage V was such that lambda m was larger than the wavelength of the particular line. Figure 3-15 shows a good example of this phenomenon.
  7. Classical perspective of light suggests that the wavelength of the scattered rays should be equal to the initial wavelength based upon electromagnetism, but multiple experiments show that the wavelength of the scattered rays was longer than the initial wavelength, which corresponds to a lower energy.
  8. Waves deliver their energy continuously, and the frequency of the wave should not change when it is introduced to a material.

Question 6:

Describe how the Compton Effect is consistent with the "quantised" perspective of light.


If the incident light can be considered as a particle of light striking another particle, the electron, then the electron will carry away some of the incident energy, leaving the recoiling X-ray with less than the original energy.
  1. The Compton Effect is consistent with the quantised perspective of light because, if you treat the incident light falling on the material as a collision between a photon of energy hc/lambda and an electron, then the electron should absorb some of the photon's energy according to conservation of energy and momentum. This loss of energy of the photon would correspond to the scattered light having a longer wavelength, which agrees with the observed Compton Effect.
  2. Compton's equation describes a quantized amount of energy being lost in the collision that depends only on the scattering angle (and the mass of the particle it collides with).
  3. The lattice structure of the array of atoms acts as a diffraction grating and filters light through in equal 3 dimensional spaces.
  4. It is the result of conservation of momentum among particles and thus demonstrated light must be quantized.
  5. the change in energy of the photon comes from an electron jumping between energy levels. since electron energy levels are known to be quantized then the change in energy levels must also be quantized and light cant be viewed continuously. mathematically this comes from the fact that for constructive interference in a diffraction pattern there must be an integer of wavelengths between waves. so looking at this the different integers quantize the change in light levels
  6. Compton assumes quantized energy levels for the incident and scattered photons, i.e., E photon = hf or hc/lambda. This assumption becomes necessary in order to obtained Compton's equation, written in the answer to question 4. This means that the energy absorbed by the electron is also some quantized energy level hc/ (lambda1- lambda2). Since we know that the Compton equation accurately predicted delta lambda for certain scattering angles, we know the assumptions made by Compton must gold.
  7. Compton explained the X-ray shift by attributing the particle-like momentum to light quanta, which has its energy dependent on the frequency of the light.Compton then derived the mathematical relationship between the shift in wavelength and the scattering angle of the X-rays by assuming that each scattered X-ray photon interacted with only one electron.
  8. Distinct, elastic collisions between photons and electrons caused changes in the electron momentum, therefore providing energy for the particle theory of light.