Quantum Physics and Nuclear Physics 13.1 Quantum Physics.
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Slide 2 Quantum Physics and Nuclear Physics 13.1 Quantum Physics Slide 3 Quantum Physics Revision When an electron falls to a lower energy level, the change in energy (E) is emitted as a photon of e-m radiation. E = E 2 E 1 The change in energy is proportional to the frequency of the emitted photon: ( E = Photon energy h = Planks constant = 6.6 x 10 -34 m 2 kgs -1 ) E = hf Slide 4 John Parkinson 3 MAX PLANCK PHOTOELECTRIC EFFECT Slide 5 The photoelectric effect The photoelectric effect is the emission of electrons from the surface of a material due to the exposure of the material to electromagnetic radiation. For example zinc emits electrons when exposed to ultraviolet radiation. If the zinc was initially negatively charged and placed on a gold leaf electroscope, the electroscopes gold leaf would be initially deflected. However, when exposed to the uv radiation the zinc loses electrons and therefore negative charge. This causes the gold-leaf to fall..- - - Gold Leaf Electroscope Slide 6 John Parkinson 5 At the end of the nineteenth century, Classical Electromagnetic Wave Theory thought of light waves as being like water waves. The waves Intensity or energy was directly proportional to the square of the Amplitude, A. A Slide 7 John Parkinson 6 Potassium metal undergoes photoemission with blue and green light, but not with red light. potassium metal e e Emission! Nothing!! Blue light Green light Red light Slide 8 John Parkinson 7 THE CLASSICAL THEORY SUGGESTS TRYING MORE INTENSE LIGHT potassium metal Nothing!!Nothing!! Slide 9 John Parkinson 8 The Classical Theory must be wrong!!!!! Slide 10 Threshold Frequency Electrons will only be emitted from zinc by photoelectric emission if the electromagnetic radiation incident upon its surface has a frequency of 1 x 10 15 Hz or above. This is called the threshold frequency of zinc. Limitation of Wave Theory of Light Wave theory would suggest that once enough visible light energy had been absorbed by the zinc, the electron would be able to escape. This is not the case. No matter how intense the incident radiation, if its frequency is below the threshold frequency for a particular material, no photoelectric emission will occur. Slide 11 Experimental observations Threshold frequency The photoelectric effect only occurs if the frequency of the electromagnetic radiation is above a certain threshold value, f 0 Variation of threshold frequency The threshold frequency varied with different materials. Affect of radiation intensity The greater the intensity the greater the number of electrons emitted, but only if the radiation was above the threshold frequency. Time of emission Electrons were emitted as soon as the material was exposed. Maximum kinetic energy of photoelectrons This depends only on the frequency of the electromagnetic radiation and the material exposed, not on its intensity. INTENSITY OF RADIATION DOES NOT ATTECT ENERGY OF EMITTED ELECTRONS Slide 12 Problems with the wave theory Up to the time the photoelectric effect was first investigated it was believed that electromagnetic radiation behaved like normal waves. The wave theory could not be used to explain the observations of the photoelectric effect in particular wave theory predicted: that there would not be any threshold frequency all frequencies of radiation should eventually cause electron emission that increasing intensity would increase the rate of emission at all frequencies not just those above a certain minimum frequency that emission would not take place immediately upon exposure the weaker radiations would take longer to produce electrons. Slide 13 Threshold Frequency Electrons will only be emitted from zinc by photoelectric emission if the electromagnetic radiation incident upon its surface has a frequency of 1 x 10 15 Hz or above. This is called the threshold frequency of zinc. Limitation of Wave Theory of Light Wave theory would suggest that once enough visible light energy had been absorbed by the zinc, the electron would be able to escape. This is not the case. No matter how intense the incident radiation, if its frequency is below the threshold frequency for a particular material, no photoelectric emission will occur. Slide 14 Photons the Quantum Model In 1900 Max Planck came up with the idea of energy being quantised in some situations. i.e. existing in small packets. In 1905 Einstein suggested that all e-m radiation is emitted in small quanta called photons rather than in a steady wave. - Intensity of radiation depends on the number of photons being emitted per second (not amplitude as suggested by the wave model). - Energy per photon depends upon its frequency: E = hf Slide 15 EinsteinsEinsteins explanation Electromagnetic radiation consisted of packets or quanta of energy called photons The energy of these photons: depended on the frequency of the radiation only was proportional to this frequency Photons interact one-to-one with electrons in the material If the photon energy was above a certain minimum amount (depending on the material) the electron was emitted any excess energy was available for electron kinetic energy Einstein won his only Nobel Prize in 1921 for this explanation. This explanation also began the field of Physics called Quantum Theory, an attempt to explain the behaviour of very small (sub-atomic) particles. Slide 16 John Parkinson 15 Quantum Theory of the Photoelectric Effect Because of the interaction of this electron with other atoms, it requires a certain minimum energy to escape from the surface. The photons are sufficiently localized, so that the whole quantum of energy [ hf ] can be absorbed by a single electron at one time. The electron can then either share its excess energy with other electrons and the ion lattice or it can use the excess energy to fly out of the metal. The minimum energy required to escape depends on the metal and is called the work function, . Slide 17 John Parkinson 16 For electron emission, the photon's energy has to be greater than the work function. The maximum kinetic energy the released electron can have is given by: E K = hf - For every metal there is a threshold frequency, f 0, where hf 0 = , that gives the photon enough energy to produce photoemission. It follows that the photo electric current is proportional to the intensity of the radiation provided the frequency of radiation is above threshold frequency. The number of photoelectrons emerging from the metal surface per unit time is proportional to the number of photons striking the surface that in turn depends on the intensity of the incident radiation E K = photon energy the work function. Slide 18 John Parkinson 17 Quantum Theory of the Photoelectric Effect In 1905 Einstein developed Plancks idea, that energy was quantised in quanta or photons, in order to explain the photoelectric effect. Electromagnetic radiation is emitted in bursts of energy photons. The energy of a photon is given by E = hf, where f is the frequency of the radiation and h is Plancks constant. [h = 6.6 x 10 -34 Js] But velocity of light = frequency times wavelength Substituting into E = hf Slide 19 John Parkinson 18 the visible spectrum frequency violet light light 400 nm red light light 700 nm uv light < 400 nm Blue photon Red photon Which photon has the most energy ????? BLUE !!! Slide 20 Photon energy (revision) photon energy (E) = h x f where h = the Planck constant = 6.63 x 10 -34 JsPlanck also as f = c / ; E = hc / Calculate the energy of a photon of ultraviolet light (f = 9.0 x 10 14 Hz) (h = 6.63 x 10 -34 Js) E = h f = (6.63 x 10 -34 Js) x (9.0 x 10 14 Hz) = 5.37 x 10 -19 J Slide 21 The photoelectric equation hf = + E Kmax where: hf = energy of the photons of electromagnetic radiation = work function of the exposed material E Kmax = maximum kinetic energy of the photoelectrons Work function, This is the minimum energy required for an electron to escape from the surface of a material Slide 22 Threshold frequency f 0 As: hf = + E Kmax If the incoming photons are of the threshold frequency f 0, the electrons will have the minimum energy required for emission and E Kmax will be zero therefore: hf 0 = and so: f 0 = / h Slide 23 Question 1 Calculate the threshold frequency of a metal if the metals work function is 1.2 x 10 -19 J. (h = 6.63 x 10 -34 Js) f 0 = / h = ( 1.2 x 10 -19 J) / (6.63 x 10 -34 Js) threshold frequency = 1.81 x 10 14 Hz Slide 24 Question 2 Calculate the maximum kinetic energy of the photoelectrons emitted from a metal of work function 1.5 x 10 -19 J when exposed with photons of frequency 3.0 x 10 14 Hz. (h = 6.63 x 10 -34 Js) hf = + E Kmax (6.63 x 10 -34 Js) x (3.0 x 10 14 Hz) = (1.5 x 10 -19 J) + E Kmax E Kmax = 1.989 x 10 -19 - 1.5 x 10 -19 = 0.489 x 10 -19 J maximum kinetic energy = 4.89 x 10 - 20 J Slide 25 The vacuum photocell Light is incident on a metal plate called the photocathode. If the lights frequency is above the metals threshold frequency electrons are emitted. These electrons passing across the vacuum to the anode constitute and electric current which can be measured by the microammeter. The photocell is an application of the photoelectric effect Slide 26 John Parkinson 25 Radiation mA Anode +ve Cathode -ve electrons The electromagnetic radiation releases electrons from the metal cathode. These electrons are attracted to the anode and complete a circuit allowing a current to flow vacuum Slide 27 John Parkinson 26 If the polarity is reversed, the pd across the tube can be increased until even the most energetic electrons fail to cross the tube to A. The milliammeter then reads zero. mA A C Radiation electrons The p.d. across the tube measures the maximum kinetic energy of the ejected electrons in electron volts. V Slide 28 Obtaining Plancks constant By attaching a variable voltage power supply it is possible to measure the maximum kinetic energy of the photoelectrons produced in the ph