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- 1. PHOTONS <ul><li>12 SACE PHYSICS-STAGE 2 </li></ul><ul><li>SECTION 3 TOPIC 3 </li></ul><ul><li>PRINCE ALFRED COLLEGE </li></ul>
- 2. WAVE VS PARTICAL THEORY <ul><li>Towards the end of the 19th century, Maxwell’s theory of electromagnetism combined and explained electric and magnetic phenomena. </li></ul><ul><li>It also predicted that e-m waves would behave in every respect like light waves. </li></ul>
- 3. WAVE VS PARTICLE THEORY <ul><li>On Christmas Eve 1899, Max Planck proposed a theory so revolutionary that the physics world was thrown into turmoil and all theories before this time are now called classical (or Newtonian). </li></ul>
- 4. WAVE VS PARTICLE THEORY <ul><li>Everything since has been called modern physics. He proposed what was known as quantum theory. </li></ul>
- 5. WAVE VS PARTICLE THEORY <ul><li>Recall that light behaves like a wave whenever it passes through a single slit (diffraction) or are superimposed on each other (interference). </li></ul><ul><li>The above are arguments that light behaves like a wave. </li></ul>
- 6. WAVE VS PARTICLE THEORY <ul><li>However, when light interacts with matter (such as electrons), it does NOT exhibit wave like properties. </li></ul><ul><li>Light tends to behave like a PARTICLE when it interacts with matter (electrons, protons etc). </li></ul><ul><li>This topic is about light behaving like a particle and the experiments that verify this. </li></ul>
- 7. THE QUANTUM HYPOTHESIS <ul><li>Classical (wave) physics could not explain the energy distribution of radiation emitted from a hot object. Objects when heated become red hot. </li></ul><ul><li>With further heating it turns white hot then blue. </li></ul><ul><li>The hotter an object becomes, the shorter the wavelength (and the higher f ). </li></ul>
- 8. THE QUANTUM HYPOTHESIS <ul><li>The actual energy distribution is a curve (a), while wave theory predicts (b). </li></ul>
- 9. THE QUANTUM HYPOTHESIS <ul><li>Planck derived an expression that was in agreement with the results. </li></ul><ul><li>He was the first to come up with light behaving like a particle. </li></ul><ul><li>His idea was that the atomic oscillators in a heated material could oscillate with only certain discrete amounts of energy. </li></ul>
- 10. THE QUANTUM HYPOTHESIS <ul><li>This means radiation is absorbed or emitted in bursts as discrete packages of energy which he called quanta rather than continuous amounts as predicted, by wave theory. </li></ul>
- 11. THE QUANTUM HYPOTHESIS <ul><li>We now use this term, quanta, in reference to a number of physical quantities. </li></ul><ul><li>Examples of quanta are... </li></ul><ul><ul><li>Gold can only have a mass that is a multiple of a gold atom. </li></ul></ul><ul><ul><li>Charge can only be a multiple of an electron. </li></ul></ul>
- 12. THE QUANTUM HYPOTHESIS <ul><li>Light also comes in “discrete packages” or quanta. </li></ul><ul><li>A quanta of light is called a PHOTON. </li></ul>
- 13. THE QUANTUM HYPOTHESIS <ul><li>Planck also assumed the minimum energy of vibration E, is proportional to the natural frequency of vibration, f . </li></ul><ul><li>If the atomic oscillator (electron) is offered less than this amount, it will accept none of the energy. </li></ul><ul><li>The electron would not go up an energy level. </li></ul>
- 14. THE QUANTUM HYPOTHESIS <ul><li>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. </li></ul><ul><li>The re-radiated energy occurs as the atomic oscillator drops back to one of its permitted energy states. </li></ul>
- 15. THE QUANTUM HYPOTHESIS <ul><li>The equation for this is: E= h f </li></ul><ul><li>h is Planck’s constant = 6.625 x 10 -34 Js </li></ul><ul><li>The small number in this constant ensures that a photon will represent a very small amount of light energy. </li></ul>
- 16. THE QUANTUM HYPOTHESIS <ul><li>From the equation c = f and rearranging to: </li></ul>
- 17. LOW INTENSITY LIGHT AND IMAGE BUILDUP <ul><li>Let’s look at Young’s Two Slit Interference Pattern. </li></ul><ul><li>As the intensity of the light source get greater (light source gets brighter), the image of the interference pattern on the screen would also get brighter. </li></ul><ul><li>As we dim the light source, the image of the interference pattern would become fainter. </li></ul>
- 18. LOW INTENSITY LIGHT AND IMAGE BUILDUP <ul><li>This is what you would expect to see on the screen if the light source was bright. </li></ul>
- 19. LOW INTENSITY LIGHT AND IMAGE BUILDUP <ul><li>However something extremely interesting occurs if you use extremely low levels of light through the double slit. </li></ul><ul><li>This would be done in a darkroom where there would be only stray ambient light. An open shutter on a camera would collect this light on the photographic film after the stray ambient light had passed through the slits. </li></ul>
- 20. LOW INTENSITY LIGHT AND IMAGE BUILDUP <ul><li>This is what you would see on the photographic film after the experiment. </li></ul><ul><li>The image looks like little pin-pricks of light. </li></ul><ul><li>We find that if we repeat this experiment many times and add the photos together... </li></ul>
- 21. LOW INTENSITY LIGHT AND IMAGE BUILDUP <ul><li>… we get the following photographic image. This is the interference pattern! </li></ul><ul><li>Thus it appears that the build up of an image is caused by the arrival at the plate of localised bundles of light energy. </li></ul>
- 22. LOW INTENSITY LIGHT AND IMAGE BUILDUP <ul><li>As more and more of these little bundles of light energy arrive at the screen the image is gradually built up. </li></ul><ul><li>These little bundles of light energy are the PHOTONS. </li></ul><ul><li>This is an excellent experiment that suggests that light has BOTH WAVE LIKE AND PARTICLE LIKE PROPERTIES. </li></ul><ul><li>Wave Partical Duality </li></ul>
- 23. THE PHOTOELECTRIC EFFECT <ul><li>The following experiment serves as evidence that LIGHT BEHAVES LIKE A PARTICLE (PHOTON) WHEN IT INTERACTS WITH MATTER. </li></ul>
- 24. THE PHOTOELECTRIC EFFECT <ul><li>Early this century, several people had noticed that light was capable of ejecting electrons from various metal surfaces. </li></ul><ul><li>Photoelectric Effect </li></ul>
- 25. THE PHOTOELECTRIC EFFECT <ul><li>This effect, known as the photoelectric effect, is used in photographer’s light meters, sound tracks of motion pictures and electric eyes used to automatically open doors. </li></ul><ul><li>Photoelectric Effect </li></ul>
- 26. THE PHOTOELECTRIC EFFECT <ul><li>Remember that metals have “free” electrons that are not tightly bound. It is these electrons that allow current and heat to flow in a metal, as the electron’s move. </li></ul>
- 27. THE PHOTOELECTRIC EFFECT <ul><li>Examples of the freeing of electrons from light energy… </li></ul><ul><ul><li>Hertz, in 1887, noticed that a spark would jump between electrodes if exposed to UV light (electrons being released from the electrode). </li></ul></ul><ul><ul><li>Other scientists noticed that the leaves of a negatively charged electroscope diverged less over time while a positively charged electroscope did not. </li></ul></ul>
- 28. THE PHOTOELECTRIC EFFECT <ul><li>This was due to the electrons “leaking” away from the electroscope as the light energy struck the top plate, allowing the electrons to escape. </li></ul>
- 29. CLASSICAL THEORY <ul><li>We will now look at the predictions made for light using classical (light behaving as a wave) physics and the actual observations that were made in experiments. </li></ul>
- 30. CLASSICAL THEORY <ul><li>CLASSICAL PREDICTION: </li></ul><ul><li>The more intense (brighter) the light, the greater the kinetic energy of ejection of the electron. Bright light would eject electrons at high speed </li></ul><ul><li>ACTUAL OBSERVATION: </li></ul><ul><li>Intensity (brightness) did not lead to high velocity electrons. Instead it led to a greater numbers of electrons being ejected from the metal. </li></ul>
- 31. CLASSICAL THEORY <ul><li>CLASSICAL PREDICTION: </li></ul><ul><li>More photoelectrons should be ejected by low frequency radiation (i.e. red) than by high frequency radiation. Classical theory considers e-m waves to be oscillating electric and magnetic fields. 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. High frequency waves would move so fast the electron would hardly begin to move in one direction before it was forced to reverse direction - not ideal for ejection. </li></ul><ul><li>ACTUAL OBSERVATION: </li></ul><ul><li>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. This was called the threshold frequency which is different for different materials. </li></ul>
- 32. CLASSICAL THEORY <ul><li>CLASSICAL PREDICTION: </li></ul><ul><li>There should be a time delay between when a radiation is incident on a surface and when the photoelectrons are ejected (See point 2) </li></ul><ul><li>ACTUAL OBSERVATION: </li></ul><ul><li>Photoelectrons were ejected instantaneously. </li></ul>
- 33. CLASSICAL THEORY <ul><li>CLASSICAL PREDICTION: </li></ul><ul><li>The radiation’s wavefront falls over the whole surface, billions of photoelectrons should be simultaneously ejected. </li></ul><ul><li>ACTUAL OBSERVATION: </li></ul><ul><li>By limiting the amount of light on a surface, a single electron could be ejected. </li></ul>
- 34. CLASSICAL THEORY <ul><li>CLASSICAL PREDICTION: </li></ul><ul><li>One velocity of ejection should be possible for radiation of one frequency. </li></ul><ul><li>ACTUAL OBSERVATION: </li></ul><ul><li>Emitted photoelectrons have a range of ejection velocities and energies. </li></ul>
- 35. CLASSICAL THEORY <ul><li>The observations made on the previous slides do NOT AGREE with the predictions made by the Classical Theory. </li></ul><ul><li>Photoelectric Effect - Changing Variables </li></ul><ul><li>Photoelectric Effect - Changing Variables 2 </li></ul><ul><li>How can we resolve this? </li></ul>
- 36. EINSTEIN’S EXPLANATION -PHOTOELECTRIC EFFECT <ul><li>In 1905 Einstein adopted quantum theory to explain the photoelectric effect and was awarded a Nobel Prize for Physics in 1921. </li></ul><ul><li>Planck also used quantum theory to explain the photoelectric effect. He said that the quantum effect occurred at the point where the radiation struck the electrons. The electron would only accept a discrete amount of energy from the incident radiation. Too little energy and the electron would accept none. </li></ul>
- 37. EINSTEIN’S EXPLANATION -PHOTOELECTRIC EFFECT <ul><li>If offered too much, the difference would be emitted as radiation. </li></ul>
- 38. EINSTEIN’S EXPLANATION -PHOTOELECTRIC EFFECT <ul><li>Einstein also said that not only was the energy absorbed and emitted by atoms in bursts but the incoming radiation was in the form of discrete entities and not a continuous wave. </li></ul><ul><li>He named these discrete entities light quanta. This was renamed photons (a quantum of radiant energy) later as they do behave like particles and in keeping with other particles, electrons, protons and neutrons. </li></ul>
- 39. EINSTEIN’S EXPLANATION -PHOTOECLECTRIC EFFECT <ul><li>Einstein’s explanation depends on the relationship E = hf </li></ul><ul><li>A UV photon would have more energy than a blue light photon as it has a higher frequency. </li></ul><ul><li>The key to his explanation is that each photon on striking an atom and being absorbed may release only one electron. It never shares its energy amongst electrons. </li></ul><ul><li>Any excess energy will be given as kinetic energy to the electron. </li></ul>
- 40. EINSTEIN’S EXPLANATION -PHOTOECLECTRIC EFFECT <ul><li>According to Einstein, only high frequency light would have enough energy ( E = h f ) to eject an electron from a metal surface. </li></ul><ul><li>Low frequency light (like red light) might not have enough energy to pull the electron away from the atom’s nucleus. </li></ul>
- 41. EINSTEIN’S EXPLANATION -PHOTOECLECTRIC EFFECT <ul><li>Imagine that electrons in an atom are at the bottom of a potential energy well that has a sloping base as shown: </li></ul>
- 42. EINSTEIN’S EXPLANATION -PHOTOECLECTRIC EFFECT <ul><li>As each electron is at a different depth, they are bound to the atom by a different amount. Each electron will then be emitted with different energies. If an electron absorbs a photon with sufficient energy, the electron can be freed. </li></ul>
- 43. EINSTEIN’S EXPLANATION -PHOTOECLECTRIC EFFECT <ul><li>The minimum amount of photon energy required to remove the least bound electron is called the work function (W) and has the units joules but eV are more commonly used. </li></ul>
- 44. EINSTEIN’S EXPLANATION -PHOTOECLECTRIC EFFECT <ul><li>The “least bound electron” is the electron in the outermost electron shell of the atom. This will be the easiest electron to pull away from the atom. </li></ul><ul><li>It is also called the “most energetic electron” because all of the remaining energy given to it will be in the form of kinetic energy which will give it the highest speed of any of the released electrons. </li></ul>
- 45. EINSTEIN’S EXPLANATION -PHOTOECLECTRIC EFFECT <ul><li>The work function is given by: W = hf o </li></ul><ul><li>f o = threshold frequency </li></ul><ul><li>The threshold frequency is the minimum frequency required to free the “least bound” electron. </li></ul>
- 46. EINSTEIN’S EXPLANATION -PHOTOECLECTRIC EFFECT <ul><li>When the photon falls on an electron with more energy than is needed to remove the bound electron, the difference in energy is transformed into kinetic energy of the electron. </li></ul><ul><li>The least bound electron is also known as the most energetic electron. </li></ul>
- 47. EINSTEIN’S EXPLANATION -PHOTOECLECTRIC EFFECT <ul><li>E incoming photon = K + Energy required for electron to escape </li></ul><ul><li>For the least bound electron, </li></ul><ul><li>E incoming photon = K (max) + W </li></ul><ul><li>hf = + + h f o </li></ul><ul><li>= hf - W </li></ul>
- 48. EINSTEIN’S EXPLANATION -PHOTOECLECTRIC EFFECT <ul><li>This is called Einstein’s photoelectric equation. </li></ul>
- 49. EXAMPLE 1 <ul><li>A certain metal has a work function of 2.0eV. Will light of wavelength 4.0 x 10 -7 m cause the ejection of photoelectrons and if so what will be their maximum velocity of ejection? </li></ul>
- 50. EXAMPLE 1 SOLUTION
- 51. QUANTUM (MODERN) PHYSICS <ul><li>The photon concept was used by Einstein to explain the experimental observations of the photoelectric effect. </li></ul><ul><li>We will now go back to the observations made in the photoelectric effect experiment and look at Einstein’s explanation using quantum physics. </li></ul>
- 52. QUANTUM (MODERN) PHYSICS <ul><li>ACTUAL OBSERVATION: </li></ul><ul><li>The (kinetic) energy of ejected photoelectrons is independent of the intensity of radiation. </li></ul><ul><li>QUANTUM EXPLANATION: </li></ul><ul><li>A greater intensity means that more photons will fall on the surface. </li></ul><ul><li>This will simply eject more electrons but NOT at a faster speed. </li></ul>
- 53. QUANTUM (MODERN) PHYSICS <ul><li>ACTUAL OBSERVATION: </li></ul><ul><li>Photoelectrons are more likely to be ejected by high frequency than low frequency radiation. </li></ul><ul><li>QUANTUM EXPLANATION: </li></ul><ul><li>The energy of a photon depends on the frequency of radiation (E = hf ). </li></ul><ul><li>A high-frequency photon has more energy and so gives more energy to the photoelectron. </li></ul><ul><li>A high frequency photon is more likely to have greater energy than the work function. </li></ul>
- 54. QUANTUM (MODERN) PHYSICS <ul><li>ACTUAL OBSERVATION: </li></ul><ul><li>Photoelectrons are ejected instantly. </li></ul><ul><li>QUANTUM EXPLANATION: </li></ul><ul><li>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 -8 s. </li></ul>
- 55. QUANTUM (MODERN) PHYSICS <ul><li>ACTUAL OBSERVATION: </li></ul><ul><li>A range of electron velocities of ejection are possible. </li></ul><ul><li>QUANTUM EXPLANATION: </li></ul><ul><li>Once the work function is subtracted, the remaining energy exists as kinetic energy. </li></ul><ul><li>Depending on which electron absorbs the photon, varying amounts of kinetic energy may be left over. </li></ul>
- 56. QUANTUM (MODERN) PHYSICS <ul><li>SUMMARY – the photoelectric effect can be best explained using the Quantum Theory (light behaving as a particle) as opposed to the Classical Theory (light behaving as a wave). </li></ul><ul><li>You would use the photoelectric effect in any question that asks you to prove that light behaves as particles (photons). </li></ul>
- 57. PLANCK’S CONSTANT <ul><li>This is a diagram of an apparatus used to investigate the characteristics of photoelectric emission. </li></ul><ul><li>It is used to try to determine Plank’s Constant (h) from E =hf </li></ul>
- 58. PLANCK’S CONSTANT <ul><li>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. </li></ul><ul><li>When the light strikes the cathode it causes photoelectrons to be emitted. </li></ul>
- 59. PLANCK’S CONSTANT <ul><li>If they cross the gap then they will create a current that will be read by a microammeter. </li></ul><ul><li>The anode is made progressively more positive attracting more photoelectrons until the saturation current is reached. </li></ul>
- 60. PLANCK’S CONSTANT <ul><li>This means that there cannot be more electrons given out from the cathode. </li></ul><ul><li>It is attracting all of the electrons being given off at the cathode. </li></ul>
- 61. PLANCK’S CONSTANT <ul><li>Note that we DO NOT vary the frequency or the intensity during the time that we are making the anode more positive. </li></ul><ul><li>During this time the current will get stronger, proof that the electrons are being emitted with different kinetic energies. </li></ul>
- 62. PLANCK’S CONSTANT <ul><li>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). </li></ul>
- 63. PLANCK’S CONSTANT <ul><li>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 (V s ). </li></ul>
- 64. PLANCK’S CONSTANT <ul><li>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). </li></ul>
- 65. PLANCK’S CONSTANT <ul><li>The most energetic electron can be written as: K (max.) = V s e = hf-W </li></ul><ul><li>Where V s e = Joules of energy </li></ul><ul><li>This can be rewritten as: </li></ul>
- 66. PLANCK’S CONSTANT <ul><li>This is in the same form as y = mx + c where h/e = m and -W/e = c </li></ul>
- 67. PLANCK’S CONSTANT <ul><li>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. </li></ul>
- 68. PLANCK’S CONSTANT <ul><li>Knowing these points leads to the value of Planck’s constant and the graph can determine the work function and the threshold frequency for a particular material being irradiated. </li></ul>
- 69. PLANCK’S CONSTANT <ul><li>If the metal is changed, the work function will change but the slope will remain constant. Hence, the threshold frequency will also change. </li></ul>____________ ____________
- 70. X-RAYS <ul><li>A German physicist, Wilhelm Roentgen (1845 - 1923) discovered a mysterious radiation in 1895 which he called x-rays. </li></ul>
- 71. X-RAYS <ul><li>This was after the algebraic symbol for an unknown quantity. He produced them from the anode end of an apparatus that had a high P.D. between its electrodes. </li></ul>
- 72. X-RAYS <ul><li>He discovered they were very penetrating and, because they were not deflected by a magnetic field they were not electrons. They must be instead electromagnetic radiation. </li></ul><ul><li>The diagram shows a X-ray tube similar to that used by Roentgen. </li></ul>
- 73. X-RAYS X-Ray Tube
- 74. X-RAYS <ul><li>The voltages used were in the range of 30 to 150 kV. The tube is made of heat resistant glass and is evacuated. </li></ul><ul><li>A step-down transformer converts household voltage to voltages capable of heating a filament to produce thermoelectrons. </li></ul><ul><li>The collimating hood turns these electrons into a beam that is accelerated by a voltage of at least 10,000V. </li></ul>
- 75. X-RAYS <ul><li>The energy the electrons have are so great that when they smash into a high m.p. target (e.g. tungsten), a lot of heat is produced. Cooling fins carries this heat away. </li></ul>
- 76. X-RAYS <ul><li>99% of all the electrons produce heat, the rest, X-rays. </li></ul><ul><li>When the electrons approach the nucleus, the electrical attraction slows down the electrons and the lost energy appears as a photon of radiation. </li></ul><ul><li>The energy and frequency depend on the closeness of the approach to the nucleus. </li></ul>
- 77. X-RAYS
- 78. X-RAYS <ul><li>This produces a continuous spectrum of x-ray frequencies. </li></ul><ul><li>The graph shows all the possible values of the emitted frequency as a continuous curve with a maximum cut off value. </li></ul>
- 79. X-RAYS <ul><li>The left hand side of the graph represents electrons that did not slow down much. They did not give off a high f x-ray. </li></ul>
- 80. X-RAYS <ul><li>The right side of the graph represents the electron that collides with the nucleus, giving off the maximum amount of energy in the form of a high frequency x-ray photon. </li></ul>
- 81. X-RAYS <ul><li>The electron which collides directly with a nucleus gives up all its energy to produce a photon with energy E = hf max or hc / min </li></ul><ul><li>This continuous radiation is called Bremsstrahlung (German for ‘braking’) radiation. It is also called the “soft” x-rays. </li></ul>
- 82. X-RAYS <ul><li>A good analogy of the electrons interacting with the tungsten atoms is to imagine the tungsten atom the size of a beach ball and the incoming electrons the size of marbles. </li></ul><ul><li>Suppose that we spread 40 beach balls (tungsten atoms) around the front oval. If we “shot” hundreds of marbles (electrons) across the oval, some marbles would pass </li></ul>
- 83. X-RAYS <ul><li>straight through between the beach balls, some would pass close to the beach balls and some would collide with the beach balls. </li></ul><ul><li>Each would give off a x-ray photon of a different frequency, producing the soft x-ray spectrum. </li></ul>
- 84. X-RAYS
- 85. X-RAYS <ul><li>What causes the high intensity lines (spikes)? </li></ul>
- 86. X-RAYS <ul><li>These are also called the hard x-rays. </li></ul><ul><li>The high intensity lines (hard x-rays) are the result of bombarding electrons colliding with inner shell electrons. </li></ul><ul><li>The shells in an atom are called the K, L, M, N etc, shells with K being the innermost. </li></ul><ul><li>An electron in each shell can have only a certain amount of energy. </li></ul>
- 87. X-RAYS <ul><li>If an electron is knocked out of the K shell to a higher energy shell, it is said to be in an excited energy state. </li></ul><ul><li>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. </li></ul><ul><li>This makes the hard x-ray for one frequency </li></ul>
- 88. X-RAYS <ul><li>If an electron falls into the K shell from the L(1st level), M(2nd level) or N(3rd level) shells, the radiation emitted is called the </li></ul><ul><li>radiation respectively. </li></ul><ul><li>If it falls into the L shell from the M or N shell, then the radiation is known as </li></ul><ul><li>This radiation has less energy than from the corresponding transitions. </li></ul>
- 89. X-RAYS <ul><li>Notice that the radiation has more energy and gives off a higher frequency photon than the photon because the </li></ul><ul><li>radiation has fallen down three energy levels. </li></ul><ul><li>The X-ray spectrum occurs as sharp lines on a continuous background. The position and number of the lines are characteristic of the target material being used. </li></ul>
- 90. X-RAYS <ul><li>This is because each material has electrons in different energy levels. </li></ul>
- 91. THE LINE SPECTRUM <ul><li>The continuous spectrum obtained can be explained. </li></ul><ul><li>The incident electron loses its kinetic energy to photon energy according to the law of conservation of energy. </li></ul><ul><li>K (incoming electron) = K (outgoing electron) + E photon </li></ul>
- 92. THE LINE SPECTRUM
- 93. THE LINE SPECTRUM <ul><li>As v f can be any value ( ), the frequency of the X-ray can be any value up to a maximum. This is obtained when all the energy is lost to the photon (the electron is stopped). </li></ul><ul><li>K (incoming electron) = E photon </li></ul><ul><li>V e = h f max = </li></ul>
- 94. THE LINE SPECTRUM <ul><li>Derivation of f max = e V/h </li></ul><ul><li>E max of X-ray photon = </li></ul><ul><li>loss of K max of electron hitting the target </li></ul><ul><li>= Work done by E field in accel voltage </li></ul><ul><li>Thus hf max = e V </li></ul><ul><li> f max = e V/h </li></ul>
- 95. INCREASING THE VOLTAGE <ul><li>If the accelerating voltage is increased, the energy of the colliding electrons is increased and the maximum frequency of the photon increases. </li></ul><ul><li>The position of the spectral lines for that target material does not alter since the energy levels of the shells are unaffected. </li></ul>
- 96. INCREASING THE VOLTAGE <ul><li>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. </li></ul>
- 97. INCREASING THE CURRENT <ul><li>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 max. frequency which is voltage dependent or the spectral lines. </li></ul>
- 98. EXAMPLE 2 <ul><li>Determine the shortest wavelength of an X-ray photon that can be liberated in an X-ray tube having an accelerating voltage of 100kV. Describe what type of interaction that the incoming electron had with the tungsten nucleus to produce this x-ray. </li></ul>
- 99. EXAMPLE 2 SOLUTION
- 100. EXAMPLE 2 SOLUTION <ul><li>This would be the most energetic photon with the highest frequency (shortest wavelength). </li></ul><ul><li>This would occur from the electron that directly collides with the tungsten nucleus. </li></ul><ul><li>Production of X-Rays </li></ul>
- 101. IS LIGHT A WAVE OR A PARTICLE? <ul><li>No experiment to date has shown light to display both wave and particle characteristics at once. </li></ul><ul><li>Young’s double slit was used with a light source so faint that an energy equivalent of only one photon was present in the tube at any one time. </li></ul>
- 102. IS LIGHT A WAVE OR A PARTICLE? <ul><li>This however meant that as a photon can only pass through one slit at a time, no superposition was possible. </li></ul><ul><li>If however, a photographic plate is left for a few weeks, the interference pattern consists of dark and bright fringes, identical to that obtained using brighter light. </li></ul>
- 103. IS LIGHT A WAVE OR A PARTICLE? <ul><li>Reflection, Refraction, Diffraction and Interference experiments suggest that light behaves like a wave . </li></ul><ul><li>Photoelectric Effect and the production of X-rays suggest that light behaves like a particle when it interacts with matter. </li></ul><ul><li>High frequency light (x-rays, gamma rays) exhibit more particle like behavour. </li></ul>
- 104. IS LIGHT A WAVE OR A PARTICLE? <ul><li>Low frequency energy (radio waves, microwaves) exhibit more wave like properties. </li></ul><ul><li>HOWEVER, even x-rays can exhibit wave like properties in a diffraction grating experiment (using crystals). </li></ul>
- 105. THE COMPTON EFFECT <ul><li>Please note: This section is not examinable except to be able to use the equation derived at the end. </li></ul><ul><li>An American scientist A. H. Compton (1892 - 1962) helped other scientists who wanted to still cling to classical physics concepts. </li></ul>
- 106. THE COMPTON EFFECT <ul><li>Compton showed photons may be made to behave like particles having momentum. </li></ul><ul><li>In 1923, he bombarded a block of graphite with X-rays. </li></ul><ul><li>He discovered that electrons were being ejected out of the block. </li></ul><ul><li>By measuring energy levels he verified the law of the conservation of energy: </li></ul>
- 107. THE COMPTON EFFECT <ul><li>E incident X-ray = E scattered X-ray + E k (electron) </li></ul><ul><li>hf o = hf + </li></ul><ul><li>If the law of conservation of momentum was to hold, the X-ray photon needed to be a particle. From Einstein: </li></ul><ul><li>E = mc 2 </li></ul>
- 108. THE COMPTON EFFECT <ul><li>This allows us to convert energy into mass. </li></ul><ul><li>The mass equivalent of the photon is . The photon does not have any real mass. The velocity of the photon is c , its momentum is: </li></ul>
- 109. THE COMPTON EFFECT <ul><li>p = mc </li></ul>
- 110. APPLICATION: X-RAYS IN MEDICINE <ul><li>X -rays have been used as a diagnostic tool almost since Roentgen’s original discovery nearly 100 years ago. </li></ul><ul><li>They are useful due to their great penetrating power which allows them to cast shadows, to varying degrees, of internal body parts. </li></ul>
- 111. APPLICATION: X-RAYS IN MEDICINE <ul><li>A typical X-ray tube used in medicine is shown below and can be compared the example in the school. </li></ul><ul><li>Visible light is focused by passing it through a glass lens which refracts the light. </li></ul>
- 112. APPLICATION: X-RAYS IN MEDICINE
- 113. APPLICATION: X-RAYS IN MEDICINE
- 114. APPLICATION: X-RAYS IN MEDICINE <ul><li>X-rays pass through glass without any significant refraction. This means other techniques must be used. </li></ul><ul><li>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. </li></ul>
- 115. APPLICATION: X-RAYS IN MEDICINE <ul><li>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. </li></ul><ul><li>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. </li></ul>
- 116. APPLICATION: X-RAYS IN MEDICINE <ul><li>The light areas, such as bone, leave a shadow. </li></ul><ul><li>As the beam is uniform, the difference in exposure is due to the different amounts of attenuation (reduction in intensity). </li></ul><ul><li>The attenuation varies depending on the thickness and type of tissue. </li></ul>
- 117. APPLICATION: X-RAYS IN MEDICINE
- 118. APPLICATION: X-RAYS IN MEDICINE <ul><li>Effect of Tissue Type </li></ul><ul><li>Two properties of tissue have an effect on X-ray attenuation: </li></ul><ul><li>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. </li></ul>
- 119. APPLICATION: X-RAYS IN MEDICINE
- 120. APPLICATION: X-RAYS IN MEDICINE
- 121. APPLICATION: X-RAYS IN MEDICINE <ul><li>A beam passing through lung tissue is only attenuated about one third as much as muscle tissue for the same thickness. </li></ul><ul><li>Bone is about 1.7 times the density of muscle and although the attenuation is greater, it is not attenuated 1.7 times greater. </li></ul><ul><li>This is because they are not chemically similar and leads into the second reason. </li></ul>
- 122. APPLICATION: X-RAYS IN MEDICINE <ul><li>Atomic Number -As tissue is not composed of pure elements, ‘effective atomic number’ is used. </li></ul><ul><li>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. </li></ul>
- 123. APPLICATION: X-RAYS IN MEDICINE <ul><li>This is why bone can be seen clearly in an X-ray and why amalgam (mercury/silver) used by dentists can be seen very clearly due their high atomic number. </li></ul>
- 124. APPLICATION: X-RAYS IN MEDICINE <ul><li>Penetrating Power (Hardness) of X-rays: </li></ul><ul><li>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. </li></ul><ul><li>To do this, X-ray photons of greater energy are required. </li></ul>
- 125. APPLICATION: X-RAYS IN MEDICINE <ul><li>From previously, the maximum energy of a X-ray is given by e where is the P.D. </li></ul><ul><li>To produce X-ray photons of greater energy, a greater P.D. is required. </li></ul><ul><li>Some X-ray machines use AC and so refers to peak value. </li></ul><ul><li>Modern diagnostic X-ray machines use between about 50 kV and 125 kV. </li></ul>
- 126. APPLICATION: X-RAYS IN MEDICINE <ul><li>X-rays are classified in terms of hardness according to the maximum energy of their photons. </li></ul><ul><li>Very penetrating X-rays with high maximum photon energy are referred to hard. </li></ul>
- 127. APPLICATION: X-RAYS IN MEDICINE <ul><li>The table below shows the percentage transmission through a thickness of 1 cm for different tissue types. </li></ul>
- 128. APPLICATION: X-RAYS IN MEDICINE <ul><li>The ratio of the percentage transmission through soft tissue to bone gives an idea of the contrast. </li></ul><ul><li>Contrast decreases for higher V or harder X-rays. Chest X-rays use hard X-rays to render the ribs transparent. Mammograms use very soft X-rays to improve the contrast in the entirely soft tissue (along with other techniques). </li></ul>
- 129. APPLICATION: X-RAYS IN MEDICINE <ul><li>Exposure Time </li></ul><ul><li>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). </li></ul><ul><li>The exposure time is then set. The shorter the time, the less likely the patient will move and blur the image. </li></ul>
- 130. APPLICATION: X-RAYS IN MEDICINE <ul><li>Long Duration Short Duration </li></ul>
- 131. APPLICATION: X-RAYS IN MEDICINE <ul><li>This does not reduce the exposure of the patient to the X-ray as a short time exposure requires a more intense beam. </li></ul><ul><li>As this can overheat the anode, there is a minimum exposure time for any image. </li></ul><ul><li>For a given hardness and area of coverage, the intensity of the beam is proportional to the number of photons per second emerging from the tube. </li></ul>
- 132. APPLICATION: X-RAYS IN MEDICINE <ul><li>This is determined by the number of electrons striking the anode and hence the filament current. </li></ul><ul><li>The tube current (in mA) multiplied by the exposure time is proportional to the total number of X-ray photons involved in the exposure. Radiographers refer to this as the ‘mA’s value’. </li></ul>
- 133. APPLICATION: X-RAYS IN MEDICINE <ul><li>The mA’s value determines the quantity of X-rays while the ‘kVp’ value determines the quality. </li></ul>

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