2. Characteristics of e/m Waves If the charge is accelerated; the magnetic field must be changing, the field depends on the velocity of the charge.
3. Characteristics of e/m Waves If the charge that produces this field is oscillating back and forward; it will generate a periodic wave, similar to that produced in a slinky spring.
4. Characteristics of e/m Waves This electromagnetic wave consists of; a changing electric field that, generates a changing magnetic field that, regenerates the electric field, and so on indefinitely.
5. Characteristics of e/m Waves The wave travels by transferring; energy from the electric field, to the magnetic field, and back again.
6. Characteristics of e/m Waves The fields oscillate at right angles; to each other in the one plane, while the wave moves perpendicularly, to both fields.
8. Characteristics of e/m Waves As the electric field reaches the receiving antenna; it exerts a force on the charges, which causes them to vibrate.
9. Characteristics of e/m Waves The wave then regenerates in the receiving antenna. This means the electrons in the receiving antenna; vibrate in the same manner, as the transmitting antenna.
10. Characteristics of e/m Waves Each vibrating electron; emits an electromagnetic wave, in one plane. The electric field; produced by a radio antenna, is in one direction.
11. Characteristics of e/m Waves If the antenna is vertical; the electric field is vertical. A wave that is orientated in a unique direction; is polarised.
12. Characteristics of e/m Waves This means the receiving antenna; must be orientated in the same plane, as the transmitting antenna. For radio waves; this is also vertical.
13. Characteristics of e/m Waves All electromagnetic waves travel at the speed of light. From previous work; the speed of a wave can be related to its frequency and wavelength by: v = f
14. Application - LADS Laser beam is directed onto ocean Two reflected beams are detected One from surface of water and one from surface of ocean The time taken for a pulse of laser light; to complete a round trip from the surface of the water, to the bottom and back again.
15. Application - LADS Knowing the speed at which the wave travels; measuring the time taken, allows us to calculate the distance travelled. S=Δv.t But depth = 1/2s
16. Application - LADS To increase the amount of area the LADS system can cover at one time; laser pulse scans across the path of the aircraft, in the green region of the spectrum.
17. Application - LADS The laser itself is very powerful; (1 MW). This compares to the school laser; 0.95 mW. The laser has both infra red beam (for height above water) and green beam (for depth of sea) The reasons the laser is so powerful include:
23. COHERENCE Coherence - two wave sources that are… Same frequency Same wavelength Maintain a constant phase relationship.
24. Incandescent light Light generated by heating a source is from oscillating charged particles. This will be in a continuous spectrum of frequencies The em waves that result are of same frequency and therefore monochromatic But have no fixed phase relationship
25. INTERFERENCE INTERFERENCE - occurs when two or more waves pass through the same space. CONSTRUCTIVE INTERFERENCE - two waves that have the same phase relationship and frequency. Example: Two waves that have overlapping crests leads to a doubling of the amplitude of the wave.
26. INTERFERENCE DESTRUCTIVE INTERFERENCE - two waves are out of step. Example: One waves crest meets another waves trough. The waves will cancel each other out. Wave Interference Example
27. INTERFERENCE A constant phase relationship is maintained in both constructive and destructive interference when the frequency of both waves is the same. We therefore say that the two sources that produced the waves are mutually coherent.
28. WATER WAVE INTERFERENCE Here is an example of two water waves interfering with each other. The two dippers are striking the water at the same time with the same frequency at S1 and S2.
29. WATER WAVE INTERFERENCE The Law of Superposition applies (sum of all waves added at a particular point). Constructive Interference (crest meets crest or trough meets trough) - waves in phase and reinforcement occurs. Resultant wave has twice the amplitude. Destructive Interference (crest meets trough) - waves half step out of phase and annulment occurs. Zero amplitude.
30. WATER WAVE INTERFERENCE As the two waves have the same frequency they will have a constant phase relationship (coherence). They therefore will have points that will always constructively interfere (ANTINODES) and destructively interfere (NODES).
31. WATER WAVE INTERFERENCE The nodes on the diagram are open circles. The antinodes are shown as black dots.
32. WATER WAVE INTERFERENCE For a point to be on a nodal line, the difference between its distance from one source and the distance from the other source must be an odd number of half wavelengths. This is called the Geometric Path Difference (G.P.D.)
33. WATER WAVE INTERFERENCE For any point on an antinodal line, the G.P.D. must be an even number of half -wavelengths. Reinforcement (antinodes) will occur at G.P.D. = m m = 0, 1, 2…..
34. WATER WAVE INTERFERENCE What if we were to reverse the phase of one source? A crest leaves S1 at the same time as a trough leaves S2. Annulment… G.P.D. = m Reinforcement … G.P.D = (m + ½)
35. LIGHT INTERFERENCE In the case of light, it is the overlapping electromagnetic waves that produce the interference patterns. It is difficult to observe interference patterns with light due its very small wavelength of around The bandwidth would be extremely small (anti nodes close together).
36. LIGHT INTERFERENCE A single slit is illuminated with monochromatic (light of all the same frequency) light. It might be all blue light or all red light. This slit becomes a point source and emits circular wavefronts. The light emerging from the slit is coherent (only one crest or trough can get through at any given time).
37. LIGHT INTERFERENCE If the double slits are equidistant from the single slit, a crest (or trough) will reach the double slits simultaneously.
38. LIGHT INTERFERENCE A sodium vapour lamp would be a good monochromatic light source if using the Young’s Slits Experiment. If you are using a LASER there is no need for the single slit as LASER light is already monochromatic and coherent.
39. LIGHT INTERFERENCE If you were to shine the double slit towards a white screen you would see alternating bands of bright and dark fringes on the screen. The bright bands would be antinodal lines, places where two crests (or troughs) were overlapping.
40. LIGHT INTERFERENCE THE DERIVATION OF d sin = m This is an essential derivation from the syllabus. d = distance between the two slits. L = distance between the slits and the screen. y = the bandwidth (distance between consecutive antinodes or consecutive nodes). Optical Path Difference (O.P.D.) = the extra difference that one of the slits is from the screen.
42. LIGHT INTERFERENCE bisects the angle by the two waves that meet at . is at right angles to in order that we have which is the extra distance or the O.P.D. between the waves.
43. LIGHT INTERFERENCE Since is very small, the angle is approximately . This means that triangle can be treated as a right angled triangle sin = or = d sin Remember that is the Optical Path Difference.
46. DIFFRACTION Diffraction is the bending of a wave as it passes near an obstacle while remaining in the same medium. This phenomena occurs in water, sound and light waves.
47. DIFFRACTION As the slit width approaches the wavelength of the water wave, the diffraction is very noticeable.
48. DIFFRACTION If light passes through an opening that is wide compared to the wavelength, the diffraction effect is small. The result is that we see a sharp shadow.
49. DIFFRACTION If the opening width approaches the wavelength of the light, the diffraction produced becomes more pronounced and the shadow becomes more fuzzy around the edges. The light is diffracted by the thin slit.
50. DIFFRACTION This can also happen when radio waves pass between two large objects. Consider two large buildings in the centre of Adelaide. FM Waves have a wavelength of 2-3 m. They therefore pass through the space between buildings with little diffraction.
51. DIFFRACTION AM Radio waves have a much longer wavelength (200-300 metres). It is at least as large as the gap between the buildings. They therefore show considerable diffraction This allows you to get good AM reception while the FM reception has “shadow zones” in cities.
52. DIFFRACTION Streetlights viewed through a dirty windscreen at night will show a diffraction pattern in the form of a cross. This is due to the fine dust particles having a very small gap between them.
53. MULTIPLE SLIT DIFFRACTION The characteristics of multiple slits can be summarised as below: Interference fringes are superimposed on the single slit diffraction pattern only when there are least two slits enabling the interference of waves to occur.
54. MULTIPLE SLIT DIFFRACTION As the number of slits increases, the diffraction pattern spreads and the intensity of each reinforcement diminishes. As the number of slits increases, each fringe becomes narrower. This results in sharper reinforcement bands.
55. MULTIPLE SLIT DIFFRACTION The central bandwidth is no longer twice that of fringe bands. The bandwidth equation can no longer be used. When there are a large number of slits, very sharp reinforcement lines occur with non-uniform spacing between them.
56. THE DIFFRACTION GRATING A large number of equally spaced parallel slits which can also be called an ‘interference grating’. There are two types: TRANSMISSION: Large number of equally spaced scratches (6000 per cm is common) are inscribed mechanically into a transparent material such as glass. Each scratch becomes an opaque line and the space in between becomes a slit.
57. THE DIFFRACTION GRATING Coherent light is directed on the diffraction grating by passing light through a collimator (light gatherer). The pattern can be seen through the telescope. The whole arrangement is called a spectrometer.
58. THE DIFFRACTION GRATING The pattern is similar to Young’s double slit pattern. The slits are narrow enough so that diffraction by each of them spreads light over a very wide angle on to a screen. Interference occurs with light waves from all slits.
59.
60. THE DIFFRACTION GRATING We use the Spectroscope to find the wavelengths of the different colours. For reinforcement Each wavelength of light (or different colour) will have a unique angle that it is diffracted to on the screen.
61. THE DIFFRACTION GRATING When m = 0, the central reinforcement line is produced and is called the zero order maximum. First order maxima occur when m = 1 and second order maxima when m = 2.
62. THE DIFFRACTION GRATING The diffraction pattern for a grating is different to that from a double slit pattern. The bright maxima are much narrower and brighter for a grating.
63.
64. THE DIFFRACTION GRATING For a grating, the waves from two adjacent slits will not be significantly out of phase but those from a slit maybe 500 away, may be exactly out of phase. Nearly all the light will cancel out in pairs this way. The more lines, the sharper the peaks will be. Double Slit Multiple Slits
65. PRODUCING SPECTRUMS PRODUCING SPECTRUMS FROM WHITE LIGHT USING A SPECTROSCOPE. If the light is not monochromatic, the angles at which the wavelengths produce their mth order maxima are different.
66. PRODUCING SPECTRUMS On either side after the central white maxima and an area of darkness, violet reinforces first as it has the smallest wavelength, then the other colours through to red. A clear first order (m = 1) continuous spectrum can be seen.
67. PRODUCING SPECTRUMS Higher order spectra become spread further and become less intense. The pattern will overlap from the third order onwards and the bandwidth formula used in the double slit cannot be used.
69. LASERS The light from these sources is perfectly coherent and is produced by a process known as Light Amplification by Stimulated Emission of Radiation (LASER). The full explanation of a laser can only be given with quantum theory.
70. LASERS The atoms of (for example) a He - Ne gas laser are optically stimulated to emit light all of the same frequency and in such a way that the waves emitted are in phase with each other.
71. LASERS The emitted light gains in intensity by being reflected many times through the active material which is being stimulated, and then being released from the laser through a partially reflecting end mirror. The resultant beam is highly monochromatic, coherent, intense and unidirectional.
72. LASERS Often, the laser light appears to be speckled when shone onto a screen or wall (such as in one of the year 12 practicals). Speckle is produced whenever a laser beam is reflected by a rough surface. It is due to the interference between light reflected in different directions from the surface.
73. LASERS This is interference due to reflection (several waves combining for amplification)
74. APPLICATION-COMPACT DISCS (CD’S) A CD is a fairly simple piece of plastic about 1.2 mm thick. The CD consists of a moulded piece of plastic that is impressed with microscopic bumps arranged as a single, continuous spiral track of data. A thin, reflective aluminium layer is placed onto the top of the disc, to cover the bumps.
75. APPLICATION-COMPACT DISCS (CD’S) A thin acrylic layer is sprayed over the aluminum to protect it. The label is then printed onto the acrylic.
78. APPLICATION-COMPACT DISCS (CD’S) A very important point is that the height of the “bumps” is approximately one quarter the wavelength of the laser light. When the laser light is passing over the “land”, all of the light is reflected off and it travels back to photoelectric cell. The photoelectric cell then produces an electric current.
79. APPLICATION-COMPACT DISCS (CD’S) This electric current then goes on to generate sound in a loudspeaker (see loudspeaker application). Now lets look at what happens when the laser light approaches a “bump”. When the light reaches a bump, half of the light is reflected off the “bump” and half of the light is reflected off the “land”.
81. APPLICATION-COMPACT DISCS (CD’S) Because the bump is ¼ of a wavelength in height, the light being reflected off the land travels one half a wavelength further. The light reaching the photoelectric cell coming from the “land” and the “bump” is out of phase. This leads to partial cancellation and a decrease in intensity. This leads to decreased current being produced.
82. APPLICATION-COMPACT DISCS (CD’S) As the laser moves along the track the intensity of the light falling on the photoelectric cell changes every time it comes into approaches or leaves a bump. It is this change in intensity which causes the fluctuation in electric current, which causes the movement of the loudspeaker and ultimately the fluctuation in sound.
83. APPLICATION-COMPACT DISCS (CD’S) USING INTERFERENCE TO KEEP A LASER ON TRACK The musical data on the CD is read from the inside out. The CD spins above the laser. After one revolution, the laser must move to the outside exactly 1.6 microns to remain on track.
84. APPLICATION-COMPACT DISCS (CD’S) When the monochromatic light passes through the diffraction grating a central beam and a first order diffracted beam will land on the CD.
85. APPLICATION-COMPACT DISCS (CD’S) The central beam is focused on the track of the CD and passes over the bumps while the two first order diffracted beams are focused on the land on either side of the bumps. One diffracted beam is slightly ahead of the other.
86. APPLICATION-COMPACT DISCS (CD’S) The laser beam is tracking correctly when the central beam is varying in intensity from 35% to 100% and the two diffracted beams have a constant intensity of 100%.
87. APPLICATION-COMPACT DISCS (CD’S) If the laser beam were to stray to the other side of its correct position, then the variation in intensity of the main beam is again reduced. The TRAILING beam will now have a reduction in intensity. The tracking mechanism “senses” that it must adjust its position up in order to get back on track.
89. THE QUANTUM HYPOTHESIS Classical (wave) physics could not explain the energy distribution of radiation emitted from a hot object. Objects when heated become red hot. With further heating it turns white hot then blue. The hotter an object becomes, the shorter the wavelength (and the higher f).
90. THE QUANTUM HYPOTHESIS The actual energy distribution is a curve (a), while wave theory predicts (b).
91. THE QUANTUM HYPOTHESIS Planck derived an expression that was in agreement with the results. He was the first to come up with light behaving like a particle. His idea was that the atomic oscillators in a heated material could oscillate with only certain discrete amounts of energy. Light also comes in “discrete packages” or quanta. A quanta of light is called a PHOTON.
92. THE QUANTUM HYPOTHESIS Planck also assumed the minimum energy of vibration E, is proportional to the natural frequency of vibration, f. If the atomic oscillator (electron) is offered less than this amount, it will accept none of the energy. The electron would not go up an energy level. If it is offered enough energy, it will accept only one photon at a time and quickly re-radiate this energy as an identical photon of e-m radiation. The re-radiated energy occurs as the atomic oscillator drops back to one of its permitted energy states.
93. THE QUANTUM HYPOTHESIS The equation for this is: E= hf h is Planck’s constant = 6.625 x 10-34 Js The small number in this constant ensures that a photon will represent a very small amount of light energy.
94.
95. As we dim the light source, the image of the interference pattern would become fainter.
96.
97. LOW INTENSITY LIGHT AND IMAGE BUILDUP … we get the following photographic image. This is the interference pattern! Thus it appears that the build up of an image is caused by the arrival at the plate of localised bundles of light energy.
98. LOW INTENSITY LIGHT AND IMAGE BUILDUP As more and more of these little bundles of light energy arrive at the screen the image is gradually built up. These little bundles of light energy are the PHOTONS. This is an excellent experiment that suggests that light has BOTH WAVE LIKE AND PARTICLE LIKE PROPERTIES.
99. CLASSICAL THEORY CLASSICAL PREDICTION: The more intense the light, the greater the kinetic energy of ejection of the electron. Bright light would eject electrons at high speed ACTUAL OBSERVATION: Intensity (brightness) led to a greater numbers of electrons being ejected from the metal.
100. CLASSICAL THEORY CLASSICAL PREDICTION: More photoelectrons should be ejected by low frequency radiation (i.e. red) than by high frequency radiation. Low frequency waves allow more time for the electron to move in one direction before the field reverses and the electron moves in the opposite direction. ACTUAL OBSERVATION: Experiments showed that high frequency (UV) radiation ejected photoelectrons more readily than low frequency. There was a minimum frequency below which no photoelectrons were ejected.
101. CLASSICAL THEORY CLASSICAL PREDICTION: There should be a time delay between when a radiation is incident on a surface and when the photoelectrons are ejected ACTUAL OBSERVATION: Photoelectrons were ejected instantaneously.
102. CLASSICAL THEORY CLASSICAL PREDICTION: The radiation’s wavefront falls over the whole surface, billions of photoelectrons should be simultaneously ejected. ACTUAL OBSERVATION: By limiting the amount of light on a surface, a single electron could be ejected.
103. CLASSICAL THEORY CLASSICAL PREDICTION: One velocity of ejection should be possible for radiation of one frequency. ACTUAL OBSERVATION: Emitted photoelectrons have a range of ejection velocities and energies.
104. PHOTOELECTRIC EFFECT The observations made on the previous slides do NOT AGREE with the predictions made by the Classical Theory. Photoelectric Effect - Changing Variables Photoelectric Effect - Changing Variables 2 How can we resolve this?
105. QUANTUM (MODERN) PHYSICS ACTUAL OBSERVATION: The (kinetic) energy of ejected photoelectrons is independent of the intensity of radiation. QUANTUM EXPLANATION: A greater intensity means that more photons will fall on the surface. This will simply eject more electrons but NOT at a faster speed.
106. QUANTUM (MODERN) PHYSICS ACTUAL OBSERVATION: Photoelectrons are more likely to be ejected by high frequency than low frequency radiation. QUANTUM EXPLANATION: The energy of a photon depends on the frequency of radiation (E = hf). A high frequency photon is more likely to have greater energy than the work function.
107. QUANTUM (MODERN) PHYSICS ACTUAL OBSERVATION: Photoelectrons are ejected instantly. QUANTUM EXPLANATION: All of the energy of the photon is given up to the electron instantly. Experimental results show that the maximum time delay for the photoelectric effect is about 10-8s.
108. QUANTUM (MODERN) PHYSICS ACTUAL OBSERVATION: A range of electron velocities of ejection are possible. QUANTUM EXPLANATION: Once the work function is subtracted, the remaining energy exists as kinetic energy. Depending on which electron absorbs the photon, varying amounts of kinetic energy may be left over.
109. PLANCK’S CONSTANT This is a diagram of an apparatus used to investigate the characteristics of photoelectric emission. It is used to try to determine Plank’s Constant (h) from E =hf
110. PLANCK’S CONSTANT The cathode (negative) and anode (positive) are sealed in an evacuated glass tube to reduce the impedance (number of collisions) of the photoelectrons reaching the anode. When the light strikes the cathode it causes photoelectrons to be emitted.
111. PLANCK’S CONSTANT If they cross the gap then they will create a current that will be read by a microammeter. The anode is made progressively more positive attracting more photoelectrons until the saturation current is reached.
112. PLANCK’S CONSTANT This means that there cannot be more electrons given out from the cathode. It is attracting all of the electrons being given off at the cathode.
113. PLANCK’S CONSTANT Note that we DO NOT vary the frequency or the intensity during the time that we are making the anode more positive. During this time the current will get stronger, proof that the electrons are being emitted with different kinetic energies.
114. PLANCK’S CONSTANT Only when you make the anode very positive do you finally attract the electrons that have very little kinetic energy (they are drifting around) due to the fact that they required a large amount of energy just to free them (their Work Function).
115. PLANCK’S CONSTANT If the anode is made negative, electrons are repelled until there is no anode current. When the current is zero, the voltage applied is called the stopping voltage (Vs).
116. PLANCK’S CONSTANT At this point even the most energetic electron (with the smallest work function and hence the most kinetic energy) will not be able to make it to the anode (due to repulsion).
117. PLANCK’S CONSTANT The most energetic electron can be written as: K (max.) = Vse = hf- W Where Vse = Joules of energy This can be rewritten as:
119. PLANCK’S CONSTANT This graph shows what happens as we change the frequency (colour) of the light and the voltage required to stop the most energetic electron for that particular frequency.
120. PLANCK’S CONSTANT If the metal is changed, the work function will change but the slope will remain constant. Hence, the threshold frequency will also change.
122. X-RAYS The voltages used were in the range of 30 to 150 kV. The tube is made of heat resistant glass and is evacuated. A step-down transformer converts household voltage to voltages capable of heating a filament to produce thermoelectrons. The collimating hood turns these electrons into a beam that is accelerated by a voltage of at least 10,000V.
124. X-RAYS This produces a continuous spectrum of x-ray frequencies. The graph shows all the possible values of the emitted frequency as a continuous curve with a maximum cut off value.
125. X-RAYS The electron which collides directly with a nucleus gives up all its energy to produce a photon with energy E = hfmax or hc/ min This continuous radiation is called Bremsstrahlung (German for ‘braking’) radiation. It is also called the “soft” x-rays.
127. X-RAYS These are also called the hard x-rays. The high intensity lines (hard x-rays) are the result of bombarding electrons colliding with inner shell electrons. The shells in an atom are called the K, L, M, N etc, shells with K being the innermost. An electron in each shell can have only a certain amount of energy. DE-excitation involves the electron falling back to fill the hole and losing energy. This energy is lost in the form of a photon that is in the frequency range of an x-ray. This makes the hard x-ray for one frequency
128. THE LINE SPECTRUM Derivation of fmax = eV/h Emax of X-ray photon = loss of Kmax of electron hitting the target = Work done by E field in accel. voltage Thus hfmax = e V fmax = eV/h
129. INCREASING THE VOLTAGE If the accelerating voltage is increased, the energy of the colliding electrons is increased and the maximum frequency of the photon increases. The position of the spectral lines for that target material does not alter since the energy levels of the shells are unaffected.
130. INCREASING THE VOLTAGE Notice that the highest intensity also moves to the right. Intensity is just a measure of the number of photons being released for that particular frequency.
131. INCREASING THE CURRENT If the filament current is increased, more thermoelectrons are liberated and so more X-ray photons are also liberated. This increases the intensity but does not alter the spectral lines or the max. frequency which is voltage dependent.
132. APPLICATION: X-RAYS INMEDICINE X -rays have been used as a diagnostic tool almost since Roentgen’s original discovery nearly 100 years ago. They are useful due to their great penetrating power which allows them to cast shadows, to varying degrees, of internal body parts.
135. APPLICATION: X-RAYS INMEDICINE X-rays pass through glass without any significant refraction. This means other techniques must be used. The X-ray film is put into a light proof cassette which is placed at right angles to the beam on the opposite side of the patient from the X-ray source. Shadows are then cast on the film. For sharp shadows, the beam must be point like and the distance between the patient and the film must be small. On a typical X-ray, the dark areas allow the X-rays to pass through the tissue to the X-ray film and so expose the film.
136. APPLICATION: X-RAYS INMEDICINE The light areas, such as bone, leave a shadow. As the beam is uniform, the difference in exposure is due to the different amounts of attenuation (reduction in intensity). The attenuation varies depending on the thickness and type of tissue.
137. APPLICATION: X-RAYS INMEDICINE Effect of Tissue Type Two properties of tissue have an effect on X-ray attenuation: Density-Attenuation is proportional to tissue density. This is useful for X-rays of bones but also for looking at soft tissue. Lung and muscle tissue are chemically similar but lung tissue is only about one third as dense as muscle.
138. APPLICATION: X-RAYS INMEDICINE A beam passing through lung tissue is only attenuated about one third as much as muscle tissue for the same thickness. Bone is about 1.7 times the density of muscle and although the attenuation is greater, it is not attenuated 1.7 times greater. This is because they are not chemically similar and leads into the second reason.
139. APPLICATION: X-RAYS INMEDICINE Atomic Number-As tissue is not composed of pure elements, ‘effective atomic number’ is used. The attenuation increases with atomic number (to the fourth power). As bone has an effective atomic number of 12 compared to lung tissue (7.6) a greater attenuation of X-rays for bone can be expected than to density alone.
140. APPLICATION: X-RAYS INMEDICINE Penetrating Power (Hardness) of X-rays: In general, to achieve good detail of bone tissue, it is necessary to use X-rays with greater penetrating power than for soft tissue for the same thickness. To do this, X-ray photons of greater energy are required.
141. APPLICATION: X-RAYS INMEDICINE the maximum energy of a X-ray is given by e where is the P.D. To produce X-ray photons of greater energy, a greater P.D. is required. Some X-ray machines use AC and so refers to peak value. Modern diagnostic X-ray machines use between about 50 kV and 125 kV.
142. APPLICATION: X-RAYS INMEDICINE The table below shows the percentage transmission through a thickness of 1 cm for different tissue types.
143. APPLICATION: X-RAYS INMEDICINE Exposure Time In taking an X-ray, the required hardness is first determined depending on the tissue type and the thickness of the tissue. This sets the P.D. (known to radiographers as the ‘peak kilovoltage’, kVp). The exposure time is then set. The shorter the time, the less likely the patient will move and blur the image.
146. WAVE BEHAVIOUR OF PARTICLES DE BROGLIE’S HYPOTHESIS Count Louis de Broglie (1892 - 1970) believed in the symmetry of nature. In 1923 he reasoned that if a photon could behave like a particle, then a particle could behave as a wave.
147. WAVE BEHAVIOUR OF PARTICLES He turned Compton’s relationship to make wavelength the subject of the equation. Compton- “a photon has momentum” De Broglie- “An electron has a wavelength”
148. WAVE BEHAVIOUR OF PARTICLES An electron creates a larger wavelength than a macroscopic object due to the fact that it has a very small mass. The wavelength of an electron is very similar to the wavelength of an x-ray. A beam of electrons should then be able to be diffracted, proving that they have wave like properties.
149. WAVE BEHAVIOUR OF PARTICLES This wavelength can be measured using a crystal diffraction grating as mentioned previously as the spacing of the atoms in the crystal is in the order of 10-10m. These waves are not caused by the particle but are connected with its motion. The wavelengths are 1000 x smaller than visible light. Electron beams in electron microscopes are used as they have greater resolving powers and hence greater magnification.
150. DAVISSON-GERMER EXPERIMENT Electrons were allowed to strike a nickel crystal. The intensity of the scattered electrons is measured for various angles for a range of accelerating voltages.
151. DAVISSON-GERMER EXPERIMENT It was found that a strong ‘reflection’ was found at θ = 50° when V = 54V. This appeared to be a place of constructive interference, suggesting that the “matter waves” from the electrons were striking the crystal lattice and diffracting into an interference pattern.
152. DAVISSON-GERMER EXPERIMENT The interatomic spacing of Nickel is close to the ‘wavelength’ of an electron. Therefore it would seem possible that electron matter waves could be diffracted. Davisson and Germer set out to verify that the electrons were behaving like a wave using the following calculations.
155. DAVISSON-GERMER EXPERIMENT Experimental Result (according to Davisson-Germer) X-ray diffraction had already shown the interatomic distance was 0.215 nm for nickel. Since θ = 50°, the angle of incidence to the reflecting crystal planes in the nickel crystal is 25°as shown below:
157. DAVISSON-GERMER EXPERIMENT dsin θ = mλ For the first order reinforcement… λ = dsinθ = (.215 x 10-9)(sin50°) = 1.65 x 10-10 m
158. DAVISSON-GERMER EXPERIMENT The close correspondence between the theoretical prediction for the wavelength by de Broglie (1.67 x 10-10 m) and the experimental results of Davidson-Germer (1.65 x 10-10 m) provided a strong argument for the de Broglie hypothesis.
159. APPLICATION – ELECTRON MICROSCOPES LIGHT MICROSCOPES A normal light microscope is based on at least two converging lenses, the objective and the eyepiece. There is a limit to how much the conventional microscope can magnify the image. This is due to diffraction.
160. APPLICATION – ELECTRON MICROSCOPES This determines the minimum distance between two points on the object that can be distinguished as separate. Instead of coming to a focus at a point, the light focuses to a small disc. Any attempt to increase the magnification just magnifies the diffraction disc. For light microscopy, the minimum distance, using light of wavelength of about 5 x 10-7 m, is about 2 x 10-7 m. This corresponds to a magnification of about 1000. Using ultraviolet light, the magnification can be increased to 3000 x.
162. APPLICATION – ELECTRON MICROSCOPES Once the wavelike properties of electrons were discovered, people realised that they had the properties that were required for high magnification; 1) they have a small wavelength and 2) they can be focused using electric or magnetic fields. Just as an X-ray tube can produce electrons, electrons can be produced for an electron microscope in the same manner by accelerating of electrons across a large P.D. This takes place in an electron gun with P.D.’s in the range of 40 kV to 100 kV.
163. APPLICATION – ELECTRON MICROSCOPES The work done by the electric field and assuming the electrons start from rest, their kinetic energy is given by qV. In the case where the accelerating potential is 60 KV, the kinetic energy is: K = qV = (1.6 x 10-19) x (60 x 103) = 9.60 x 10-15 J. To determine the wavelength of the electrons, the de Broglie relationship is used, = h/p. The momentum must first be determined from the kinetic energy: K = ½mv2 = ½m2v2/m = p2/2m
164. APPLICATION – ELECTRON MICROSCOPES And so the momentum can be determined by: P = = P = 1.32 x 10-22 kgms-1
