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Urna Semper Group

UrnaSemper

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01.05.14

LabReport

PhotoelectricEffect

Background

Einstein suggested this experiment in 1905, it is of great importanceas it provided the very first quantum theory experimentalverification that was convincing enough, it was in 1921 that hereceived the Nobel prize for his theory. However, it was Hertz whoobserved the phenomenon of photoemissions of electrons ,later on in1900, Lenard identified the particles emitted as electrons andstudied their current(energy and numbers)of the emittedphotoelectrons as a function of the wavelength of the incident lightand its intensity. However, it was impossible to explain using thewave theory of light.

Einstein suggested light is propagated in tiny discrete particlesflying through space like bullets in the same way it is emitted andabsorbed as Planck stated. During the time made his suggestion, therewas not enough evidence to prove nor disapprove his theory. However,Millikan made very precise measurements and with his results, theexperiment was verified beyond any doubt.

As light contains energy, it is the energy released from the sun thatcauses weather, drives ocean currents and subsequently allows life toexist on the planet earth. It is the same transfer of energy fromlight that allows photovoltaic cells, eyesight and in plants,photosynthesis. All this goes to show how important a correctdescription of the interaction between light and matter is.

Theory

You will be able to repeat the most important part of the experimentthat was used to establish the quantum theory of radiation with theavailable equipments. With the photocathode being irradiated bylight of one color(quasi-monochromatic light) or wavelength, avoltage whose purpose is to oppose the energy of the emittedphotoelectrons is applied in between the anode and the cathode. eVthe kinetic energy lost (or potential energy gained), wheree is the charge of the electron while V is the voltageor potential difference between potential difference or voltagebetween the anode and cathode. The voltage that is needed to “just”stop the current flow Vs is thusdirectly proportional to the maximum kinetic energy of the emittedphotoelectron (a good example is that of a roller coaster just comingto a stop at the top of a hill here voltage changes as change theheight of the hill)

Itwas from Planck`s quantum ideas, ( his description of radiation froma blackbody) that Einstein postulated that light consists of photonswhich are basically a stream of discrete bundles of energy. Hecontinued to state that the energy, E, posed by each photon is givenby

where, is the frequency of the light, h the Planck’sconstant, and c the standard velocity of light in vacuum and λ is the wavelength of the light. Therefore, from theassumption, it follows that photoelectric effect occurs as a resultof each photon transferring all its energy to a single electron inthe metal. Some of the transferred energy is used to tear free theelectron from the metal ( this energy is referred to as the workfunction, , any remaining excess energy provides kineticenergy to the electron which has been already ejected. Using theprevious results for the maximum kinetic energy and also accountingfor all the energies

Work function varies in different material and is least for alkalimetals (this apparatus uses sodium). In order to observephotoelectric effect, light must be such that ,h&gt , this is referred to as the threshold frequency. Photoelectriceffect in alkalis is seen at frequencies of visible light due to thenature of their work functions

Inorder to obtain accurate results, the measurements of very smallphotocurrents is necessary. Daedelon Corp`s &quotPhotoelectriceffect &quot apparatus contains the necessary electronics andammeter required for this.

Theoryof Operation

In this experiment, light whose frequency is known is illuminated onto the alkali metal surface(sodium in this case) which is acting asthe photocathode placed in an evacuated tube. (This is so as to keepthe surface clean and also prevent any unwanted collision such asthose of molecules present in air and photoelectrons). Electrons arethen ejected from the cathode travelling towards the anode, somereach the collector hence as a result producing a photoelectriccurrent, I, the figures below illustrate this clearly.

Figure: Illustrating Schematic in 3 distinct parts

The collector (anode) can be turned to negative (reverse bias) withrespect to the cathode so as to repel electrons hence only thoseelectrons that leave the emitter surface containing initial kineticenergy that is greater than the potential difference between theanode and cathode reach the collector and register a current.However, the potential p.d can be varied upwards until no electronsare able to reach the collector and hence the current issubsequently stopped. This is the stopping potential Vs.

By measuring the Vs, for varying light frequencies ,v, thisequation can in turn be verified experimentally hence by plotting agraph of stopping voltage vs. light frequencies, it is possible toidentify the values of h and .

Purpose

To determine the stopping voltage associated with differentwavelengths of light, test Einstein’s theory of the photoelectriceffect for any inaccuracies, and also determine a value of (Planck’sconstant),h.

Optional Pre-lab

Determine the quantity hc in SI units and also in units ofeV-Å. (1 eV is 1.6 x 10-19 J, Angstroms are bythemselves a unit of length and 1 Å= 10-10 m). The dashsimply means “multiply” here as a unit of torque is N-m.

The red He-Ne laser that is used in this lab in theory produces lightthat has a wavelength of 6328 Å. Find the energy per photon andfrequency of this light.

In most cases, it is advisable to speak about the wave-numberdefined as 1/ and normally quoted in unit of cm-1. Ifa visible light is produced from wavelength range of 4000 to 6500 Å,calculate the range in terms of wave-number. (It is howeverimportant to note that the wave-number as defined here varies fromthe wave-vector which is 2/.)

Safety

do not look directly at the mercury source and shield other lab usersfrom the light. Be sure to protective goggles and do not wearglasses. Avoiding exposing the photocathode to any light unless itis filtered. Avoid laser contact with eyes. Do not touch the mercurytube and its surrounding shielding s they get quite hot.

Questions

Beginning with the plate made of sodium. Keep all the parametersconstant except for the colour (wavelength) of the light and displayall the graphs available.

  1. Have the light source turned on at very low intensity and battery set to ZERO volts. Vary the wavelength of the light source (from Infra Red to Ultra Violet) until electrons just begin to be ejected from the sodium surface. State the wavelength and note the speed of the electrons. What is the corresponding frequency of the electromagnetic wave? Why is it called threshold frequency?

Intensityis steadily set at a constant 1%. Wavelength = 370-395 nm, energy =1eV, speed of electrons = of different speed, some fast and someslow. The corresponding frequency will be 7.59 1014Hz – 8.11 1014Hz. It is called threshold frequency because it is the minimumfrequency needed in order for the photoelectric to take place.

  1. Repeat the instruction 1 above but allow the light to shine on the metal for a longer time before the wavelength is varied. Is your finding different as found in 1? Justify your finding.

Yes, wavelength = 400nm (longer). The longer the light shines onthe metal, the more photons to give energy to the electrons in themetal.

  1. Repeat the instruction 1 above again but vary the intensity of light this time. Is your finding different as found in 1 and 2?

Yes. The wavelength becomes longer (about 540 nm).

  1. As you shorten the wavelength of the light source, what change did you notice about electron speed? Explain the possible cause of the change.

The electron speeds increases as high energy is transferred to theelectrons,

  1. Tabulate the wavelength required to just start a current flow for the 6 available surfaces. (Note: Be sure battery voltage is set to zero.) intensity is set for 5%

Surface

Wavelength (nm)

Surface

Wavelength (nm)

Sodium

491

Platinum

185

Zinc

270

Calcium

397

Copper

248

Element X.

312

  1. Arrange the surfaces in the order of the least to the most optically sensitive.

Platinum,copper, zinc, Element X, calcium, sodium.

  1. What is the probable composition of the unknown surface?

Anymaterial which work function in between Ca &amp Zn (Mg, Th, Gd, Li,Ce, Sm, Nd, Sc).

  1. Adjust the battery to +8.00 V and shine a 400 nm bright light (intensity = 100%) on a sodium surface. What happens to the electrons as you reduce the voltage of the battery from +8.00 V to -8.00 V.

The electrons move very fast to the collector at first. At about-0.20 V, electrons show deceleration generally and some of theelectrons start moving back into the sodium surface. At -0.80 V, allthe electrons move back towards the sodium surface before barelyreaching the collector.

  1. Find the work function calcium using a plot of maximum photoelectron energy against frequency.

  1. State the stopping potential of the surfaces of sodium and calcium with the same settings as in instruction 8.

Surface

Stopping Potential (V)

Sodium

-0.80

Calcium

-0.20

  1. Find the maximum kinetic energy of electrons of 400 nm bright light for the sodium and calcium surfaces based on the data obtained in instructions 8 and 10.

Surface

Calculation

Maximum K.E.

Sodium

KE max = eV

1.3 10-19 ms-1

Calcium

3.2 10-20 ms-1

  1. Based on the graph of electron energy versus light frequency obtained for sodium target, estimate the value of the Planck’s constant. Find the percentage of discrepancy between the value obtained and the actual value as well.

Forf = 1.5 1015Hz, electron energy = 4 eV

  • 4 eV = h(1.5 1015) + Wo – (a)

Forf = 3.0 1015Hz, electron energy = 10 eV

  • 10 eV = h(3.0 1015) + Wo – (b)

(b)– (a) :1.5 1015h = 6 eV

h= 6.4 10-34Js

Percentageof discrepancy =

Discussion

The aims of the were To be able to explain how the photoelectriceffect experiment works and why a photon model of light is necessaryto explain the results, the experiment revealed that Photoemissiondepends on the wavelength/frequency of the light source, of which theshorter wavelength the higher energy of electrons emitted with athreshold of frequency which is different for different materials .In addition after studying the effect of intensity of light onphotoelectric experiment it was noted that the increase in intensitywill slightly increase the wavelength required for photoelectricemission and thus increase the current in the circuit. Stoppingvoltage does not depend on the intensity of the incident light. Therelation between frequency of light, f and the maximum kineticenergy K.Emax of the electron and the work function, Woof a given target can be expressed as

The estimated value of Planck’s constant, h is 6.4 10-34 Js which is 3.41% smaller than the actual valuewhich was also an aim of the experiment.

Works Cited.

Knight Physics for Scientists and Engineers, pp. 1220-1228.

Beiser Concepts of Modern Physics 6th ed. pp.62-67,

Tipler and Llewellyn Modern Physics 4th ed., pp.141-147,

Hecht Optics 4th ed. pp. 50-56.

Knoll, Glenn F. (1999). Radiation Detection and Measurement. NewYork: Wiley. p. 49