Understanding Energy Levels & Quantum Nature of Light: Planck's Theory & Photoelectric, Lecture notes of Law

Download Understanding Energy Levels & Quantum Nature of Light: Planck's Theory & Photoelectric and more Lecture notes Law in PDF only on Docsity! h/e Apparatus and h/e Apparatus Accessory Kit 012-04049J 2 ® Planck's Quantum Theory By the late 1800's many physicists thought they had ex- plained all the main principles of the universe and discov- ered all the natural laws. But as scientists continued work- ing, inconsistencies that couldn't easily be explained be- gan showing up in some areas of study. In 1901 Planck published his law of radiation. In it he stated that an oscillator, or any similar physical system, has a discrete set of possible energy values or levels; en- ergies between these values never occur. Planck went on to state that the emission and absorption of radiation is associated with transitions or jumps be- tween two energy levels. The energy lost or gained by the oscillator is emitted or absorbed as a quantum of radiant energy, the magnitude of which is expressed by the equa- tion: E = h ν where E equals the radiant energy, ν is the frequency of the radiation, and h is a fundamental constant of nature. The constant, h, became known as Planck's constant. Planck's constant was found to have significance beyond relating the frequency and energy of light, and became a cornerstone of the quantum mechanical view of the suba- tomic world. In 1918, Planck was awarded a Nobel prize for introducing the quantum theory of light. The Photoelectric Effect In photoelectric emission, light strikes a material, causing electrons to be emitted. The classical wave model pre- dicted that as the intensity of incident light was increased, the amplitude and thus the energy of the wave would in- crease. This would then cause more energetic photoelec- trons to be emitted. The new quantum model, however, predicted that higher frequency light would produce higher energy photoelectrons, independent of intensity, while increased intensity would only increase the number of electrons emitted (or photoelectric current). In the early 1900s several investigators found that the kinetic energy of the photoelectrons was dependent on the wave- length, or frequency, and independent of intensity, while the magnitude of the photoelectric current, or number of electrons was dependent on the intensity as predicted by the quantum model. Einstein applied Planck's theory and explained the photoelectric effect in terms of the quantum model using his famous equation for which he received the Nobel prize in 1921: E = h ν = KE max + W O where KE max is the maximum kinetic energy of the emit- ted photoelectrons, and W O is the energy needed to re- move them from the surface of the material (the work function). E is the energy supplied by the quantum of light known as a photon. The h/e Experiment A light photon with energy hν is incident upon an elec- tron in the cathode of a vacuum tube. The electron uses a minimum W O of its energy to escape the cathode, leaving it with a maximum energy of KE max in the form of kinetic energy. Normally the emitted electrons reach the anode of the tube, and can be measured as a photoelectric current. However, by applying a reverse potential V between the anode and the cathode, the photoelectric current can be stopped. KE max can be determined by measuring the mini- mum reverse potential needed to stop the photoelectrons and reduce the photoelectric current to zero.* Relating kinetic energy to stopping potential gives the equation: KE max = Ve Therefore, using Einstein's equation, h ν = Ve + W O When solved for V, the equation becomes: V = (h/e) ν - (W O /e) If we plot V vs ν for different frequencies of light, the graph will look like Figure 2. The V intercept is equal to - W O /e and the slope is h/e. Coupling our experimental de- termination of the ratio h/e with the accepted value for e, 1.602 x 10-19 coulombs, we can determine Planck's constant, h. Background Theory *NOTE: In experiments with the PASCO h/e Ap- paratus the stopping potential is measured directly, rather than by monitoring the photoelectric current. See the Theory of Operation in the Technical Infor- mation section of the manual for details. Figure 2. The graph of V vs. ν Stopping Potential V Frequency ν Slope = h/e 012-04049J h/e Apparatus and h/e Apparatus Accessory Kit 13 ® Theory of Operation In experiments with the h/e Apparatus, monochromatic light falls on the cathode plate of a vacuum photodiode tube that has a low work function, W 0 . Photoelectrons ejected from the cathode collect on the anode. The photodiode tube and its associated electronics have a small capacitance which becomes charged by the photo- electric current. When the potential on this capacitance reaches the stopping potential of the photoelectrons, the current decreases to zero, and the anode-to-cathode volt- age stabilizes. This final voltage between the anode and cathode is therefore the stopping potential of the photoelectrons. To let you measure the stopping potential, the anode is connected to a built-in amplifier with an ultrahigh input impedance (> 1013 Ω), and the output from this amplifier is connected to the output jacks on the front panel of the apparatus. This high impedance, unity gain (Vout/Vin = 1) amplifier lets you measure the stopping potential with a digi- tal voltmeter. Due to the ultra high input impedance, once the capacitor has been charged from the photodiode current it takes a long time to discharge this potential through some leak- age. Therefore a shorting switch labeled “PUSH TO Zero” enables the user to quickly bleed off the charge. However, the op-amp output will not stay at 0 volts after the switch is released since the op-amp input is floating. Due to variances in the assembly process, each appara- tus has a slightly different capacitance. When the zero switch is released, the internal capacitance along with the user's body capacitance coupled through the switch is enough to make the output volatge jump and/or os- cillate. Once photoelectrons charge the anode the input voltage will stabilize. Technical Information