October 29PHYSICS 2012ubmitted by: - Swarup Kumar Boro ass: - XII
Contents1. Photoelectric Effect2. Laws of Photoelectric Emission3. The Classical Wave Explanation4. Hertz’s Observations5. Lenard’s Observations6. Einstein’s Photoelectric Equation:7. Application of Photoelectric Effect:8. de Broglie wave:9. Davisson and Germer Experiment
Photoelectric EffectThe photoelectric effect posed a significant challenge tothe study of optics in the latter portion of the 1800s. Itchallenged the classical wave theory of light, which wasthe prevailing theory of the time. It was the solution tothis physics dilemma that catapulted Einstein intoprominence in the physics community, ultimately earninghim the 1921 Nobel Prize. Though originally observed in 1839, the photoelectriceffect was documented by Heinrich Hertz in 1887 in apaper to the Annalen der Physik. It was originally calledthe Hertz effect, in fact, though this name fell out of use.
When a light source (or, more generally, electromagneticradiation) is incident upon a metallic surface, the surfacecan emit electrons. Electrons emitted in this fashion arecalled photoelectrons (although they are still justelectrons). This is depicted in the image to the right.Setting Up the PhotoelectricEffect To observe the photoelectric effect, you create avacuum chamber with the photoconductive metal at oneend and a collector at the other. When a light shines onthe metal, the electrons are released and move through thevacuum toward the collector. This creates a current in thewires connecting the two ends, which can be measuredwith an ammeter. (A basic example of the experiment canbe seen by clicking on the image to the right, and thenadvancing to the second image available.) By administering a negative voltage potential (theblack box in the picture) to the collector, it takes moreenergy for the electrons to complete the journey andinitiate the current. The point at which no electrons makeit to the collector is called the stopping potential Vs, and
can be used to determine the maximum kinetic energyKmax of the electrons (which have electronic charge e) byusing the following equation:Kmax = eVsIt is significant to note that not all of the electrons willhave this energy, but will be emitted with a range ofenergies based upon the properties of the metal beingused. The above equation allows us to calculate themaximum kinetic energy or, in other words, the energy ofthe particles knocked free of the metal surface with thegreatest speed, which will be the trait that is most usefulin the rest of this analysis.
Laws of Photoelectric Emission i) For a given substance, there is a minimum value of frequency of incident light called threshold frequency below which no photoelectric emission is possible, howsoever, the intensity of incident light may be. ii) The number of photoelectrons emitted per second (i.e. photoelectric current) is directly proportional to the intensity of incident light provided the frequency is above the threshold frequency.iii) The maximum kinetic energy of the photoelectrons is directly proportional to the frequency provided the frequency is above the threshold frequency.iv) The maximum kinetic energy of the photoelectrons is independent of the intensity of the incident light. v) The process of photoelectric emission is instantaneous. I.e. as soon as the photon of suitable frequency falls on the substance, it emits photoelectrons.vi) The photoelectric emission is one-to-one. i.e. for every photon of suitable frequency one electron is emitted.
The Classical Wave ExplanationIn classical wave theory, the energy of electromagneticradiation is carried within the wave itself. As theelectromagnetic wave (of intensity I) collides with thesurface, the electron absorbs the energy from the waveuntil it exceeds the binding energy, releasing the electronfrom the metal. The minimum energy needed to removethe electron is the work function phi of the material. (Phiis in the range of a few electron-volts for most commonphotoelectric materials.)Three main predictions come from this classicalexplanation: 1. The intensity of the radiation should have a proportional relationship with the resulting maximum kinetic energy. 2. The photoelectric effect should occur for any light, regardless of frequency or wavelength. 3. There should be a delay on the order of seconds between the radiation’s contact with the metal and the initial release of photoelectrons.
The Experimental ResultBy 1902, the properties of the photoelectric effect werewell documented. Experiment showed that: 1. The intensity of the light source had no effect on the maximum kinetic energy of the photoelectrons. 2. Below a certain frequency, the photoelectric effect does not occur at all. 3. There is no significant delay (less than 10-9 s) between the light source activation and the emission of the first photoelectrons.
Hertz’s ObservatiOnsThe phenomenon of photoelectric effect was discoveredby Heinrich Hertz in 1887. While performing anexperiment for production of electromagnetic waves bymeans of spark discharge, Hertz observed that sparksoccurred more rapidly in the air gap of his transmitterwhen ultraviolet radiations was directed at one of themetal plates. Hertz could not explain his observations butother scientists did it. They arrived at the conclusion thatthe cause was the emission of electron from metal platedue to incidence of high frequency light. This isphotoelectric effect.
Lenard’s ObservatiOnsPhillip Lenard observed that when ultraviolet radiationswere made incident on the emitter plate of an evacuatedglass tube enclosing two metal plates (called electrodes),current flows in the circuit, but as soon as ultravioletradiation falling on the emitter plate was stopped, thecurrent flow stopped. These observations indicate thatwhen ultraviolet radiations fall on the emitter (cathode)plate C, the electrons are ejected from it, which areattracted towards anode plate A. The electrons flowthrough the evacuated glass tube, complete the circuit andcurrent begins to flow in the circuit. Then Hallwach’s andLenard studied the phenomenon in detail.Hallwach’s studied further by taking a zinc plate and anelectroscope. The zinc plate was connected to anelectroscope. He observed that :(i) When an uncharged zinc plate was irradiated byultraviolet light, the zinc plate acquired positive charge.(ii) When a positively charged zinc plate is illuminated byultraviolet light, the positive charge of the plate wasincreased.(iii) When a negatively charged zinc plate was irradiatedby ultraviolet light, the zinc plate lost its charge.
All these observations show that when ultraviolet lightfalls on zinc plate, the negatively charged particles(electrons) are emitted.Further study shows that different metals emit electronsby different electromagnetic radiations. For example thealkali metals (e.g., sodium, cesium, potassium etc.) emitelectrons when visible light is incident on them. Theheavy metals (such as zinc, cadmium, magnesium etc.)emit electrons when ultraviolet radiation is incident onthem.Cesium is the most sensitive metal for photoelectricemission. It can emit electrons with less-energetic infraredradiation.In photoelectric effect the light energy is converted intoelectrical energy.
einstein’s PHOtOeLectricEquation: When a photon of energy hν falls on a metal surface,the energy of the photon is absorbed by the electron and isused in two ways:i) A part of energy is used to overcome the surface barrier and come out of the metal surface. This part of the energy is called ‘work function’ (Ф = hν0).ii) The remaining part of the energy is used in giving a velocity ‘v’ to the emitted photoelectron. This is equal to the maximum kinetic energy of the photoelectrons ( ½ mv2max ) where ‘m’ is mass of the photoelectron. According to law of conservation of energy, hν = Ф + ½ mv2max = hν0 + ½ mv2max ½ mv2max = h (ν - ν0)
Application of Photoelectric Effect: 1. Automatic fire alarm 2. Automatic burglar alarm 3. Scanners in Television transmission 4. Reproduction of sound in cinema film 5. In paper industry to measure the thickness of paper 6. To locate flaws or holes in the finished goods 7. In astronomy 8. To determine opacity of solids and liquids 9. Automatic switching of street lights 10. To control the temperature of furnace 11. Photometry 12. Beauty meter – To measure the fair complexion of skin 13. Light meters used in cinema industry to check thelight 12. Photoelectric sorting
de Broglie wave: According to de Broglie, a moving material particle can be associated with a wave. i.e. a wave can guide the motion of the particle. The waves associated with the moving material particles are known as de Broglie waves or matter waves. Expression for de Broglie wave: According to quantum theory, the energy of the photon isAccording to Einstein’s theory, the energy of the photonisE=mc2So,
Or Where p = mc is momentum of a photonIf instead of a photon, we have a material particle of massm moving with velocity v, then the equation becomes . This is the expression for de Brogliewavelength.Conclusion: i) de Broglie wavelength is inversely proportional to the velocity of the particle. If the particle moves faster, then the wavelength will be smaller and vice versa.ii) If the particle is at rest, then the de Broglie wavelength is infinite. Such a wave cannot be visualized.iii) de Broglie wavelength is inversely proportional to the mass of the particle. The wavelength associated with a heavier particle is smaller than that with a lighter particle.
iv) de Broglie wavelength is independent of the charge of the particle. Davisson and Germer Experiment A beam of electrons emitted by the electron gun ismade to fall on Nickel crystal cut along cubical axis at aparticular angle. The scattered beam of electrons is received by thedetector which can be rotated at any angle. The energy of the incident beam of electrons can bevaried by changing the applied voltage to the electrongun. Intensity of scattered beam of electrons is found tobe maximum when angle of scattering is 50° and theaccelerating potential is 54 VElectron diffraction is similar to X-ray diffraction.Bragg’s equation 2dsinθ = nλ givesλ = 1.65 Å