1、36th International Physics Olympiad. Salamanca (Espaa) 2005 Exp. Page 1 of 11 R.S.E.F. PLANCKS CONSTANT IN THE LIGHT OF AN INCANDESCENT LAMP In 1900 Planck introduced the hypothesis that light is emitted by matter in the form of quanta of energy h. In 1905 Einstein extended this idea proposing that

2、once emitted, the energy quantum remains intact as a quantum of light (that later received the name photon). Ordinary light is composed of an enormous number of photons on each wave front. They remain masked in the wave, just as individual atoms are in bulk matter, but h the Plancks constant reveals

3、 their presence. The purpose of this experiment is to measure Plancks constant. A body not only emits, it can also absorb radiation arriving from outside. Black body is the name given to a body that can absorb all radiation incident upon it, for any wavelength. It is a full radiator. Referring to el

4、ectromagnetic radiation, black bodies absorb everything, reflect nothing, and emit everything. Real bodies are not completely black; the ratio between the energy emitted by a body and the one that would be emitted by a black body at the same temperature, is called emissivity, , usually depending on

5、the wavelength. Planck found that the power density radiated by a body at absolute temperature T in the form of electromagnetic radiation of wavelength can be written as ()1 /5 1 2 = Tc e c u (1) where c1 and c2 are constants. In this question we ask you to determine c2 experimentally, which is prop

6、ortional to h. For emission at small , far at left of the maxima in Figure F-1, it is permissible to drop the -1 from the denominator of Eq. (1), that reduces to /5 1 2 Tc e c u = (2) The basic elements of this experimental question are sketched in Fig. F-2. The emitter body is the tungsten filament

7、 of an incandescent lamp A that emits a wide range of s, and whose luminosity can be varied. The test tube B contains a liquid filter that only transmits a thin band of the visible spectrum around a value 0 (see Fig. F-3). More information on the filter properties will be found in page 5. Finally, t

8、he transmitted radiation falls upon a photo resistor C (also known as LDR, the acronym of Light Dependent Resistor). Some properties of the LDR will be described in page 6. The LDR resistance R depends on its illumination, E, which is proportional to the filament power energy density 0 0 Eu Ru RE wh

9、ere the dimensionless parameter is a property of the LDR that will be determined in the experiment. For this setup we finally obtain a relation between the LDR resistance R and the filament temperature T Tc ecR 02 / 3 = (3) that we will use in page 6. In this relation c3 is an unknown proportionalit

10、y constant. By measuring R as a function on T one can obtain c2, the objective of this experimental question. F-2 A B C F-3 u 0 F-1 u T3 T2 T1 36th International Physics Olympiad. Salamanca (Espaa) 2005 Exp. Page 2 of 11 R.S.E.F. DESCRIPTION OF THE APPARATUS The components of the apparatus are shown

11、 in Fig. F-4, which also includes some indications for its setup. Check now that all the components are available, but refrain for making any manipulation on them until reading the instructions in the next page. EQUIPMENT: 1. Platform. It has a disk on the top that holds a support for the LDR, a sup

12、port for the tube and a support for an electric lamp of 12 V, 0.1 A. 2. Protecting cover. 3. 10 turns and 1 k potentiometer. 4. 12 V battery. 5. Red and black wires with plugs at both ends to connect platform to potentiometer. 6. Red and black wires with plugs at one end and sockets for the battery

13、at the other end. 7. Multimeter to work as ohmmeter. 8. Multimeter to work as voltmeter. 9. Multimeter to work as ammeter. 10. Test tube with liquid filter. 11. Stand for the test tube. 12. Grey filter. 13. Ruler. An abridged set of instructions for the use of multimeters, along with information on

14、the least squares method, is provided in a separate page. F-4 1 2 3 6 7 10 11 4 5 8 9 13 12 A V 36th International Physics Olympiad. Salamanca (Espaa) 2005 Exp. Page 3 of 11 R.S.E.F. SETTING UP THE EQUIPMENT Follow these instructions: Carefully make the electric connections as indicated in Fig. F-4,

15、 but do not plug the wires 6 to the potentiometer. By looking at Fig. F-5, follow the steps indicated below: 1. Turn the potentiometer knob anticlockwise until reaching the end. 2. Turn slowly the support for the test tube so that one of the lateral holes is in front of the lamp and the other in fro

16、nt of the LDR. 3. Bring the LDR nearer to the test tube support until making a light touch with its lateral hole. It is advisable to orient the LDR surface as indicated in Fig. F-5. 4. Insert the test tube into its support. 5. Put the cover onto the platform to protect from the outside light. Be sur

17、e to keep the LDR in total darkness for at least 10 minutes before starting the measurements of its resistance. This is a cautionary step, as the resistance value at darkness is not reached instantaneously. F-5 2 3 5 1 4 36th International Physics Olympiad. Salamanca (Espaa) 2005 Exp. Page 4 of 11 R

18、.S.E.F. Task 1 Draw in Answer Sheet 1 the complete electric circuits in the boxes and between the boxes, when the circuit is fully connected. Please, take into account the indications contained in Fig. F-4 to make the drawings. Measurement of the filament temperature The electric resistance RB of a

19、conducting filament can be given as S l RB= (4) where is the resistivity of the conductor, l is the length and S the cross section of the filament. This resistance depends on the temperature due to different causes such as: Metal resistivity increases with temperature. For tungsten and for temperatu

20、res in the range 300 K to 3655 K, it can be given by the empirical expression, valid in SI units, 83. 08 1005. 3=T (5) Thermal dilatation modifies the filaments length and section. However, its effects on the filament resistance will be negligible small in this experiment. From (4) and (5) and negle

21、cting dilatations one gets 83. 0 B RaT = (6) Therefore, to get T it is necessary to determine a. This can be achieved by measuring the filament resistance RB,0 at ambient temperature T0. Task 2 a) Measure with the multimeter the ambient temperature T0. b) It is not a good idea to use the ohmmeter to

22、 measure the filament resistance RB,0 at T0 because it introduces a small unknown current that increases the filament temperature. Instead, to find RB,0 connect the battery to the potentiometer and make a sufficient number of current readings for voltages from the lowest values attainable up to 1 V.

23、 (It will prove useful to make at least 15 readings below 100 mV.) At the end, leave the potentiometer in the initial position and disconnect one of the cables from battery to potentiometer. Find RB for each pair of values of V and I, translate these values into the Table for Task 2,b) in the Answer

24、 Sheets. Indicate there the lowest voltage that you can experimentally attain. Draw a graph and represent RB in the vertical axis against I. c) After inspecting the graphics obtained at b), select an appropriate range of values to make a linear fit to the data suitable for extrapolating to the ordin

25、ate at the origin, RB,0. Write the selected values in the Table for Task 2, c) in the Answer Sheets. Finally, obtain RB,0 and RB,0. d) Compute the numerical values of a and a for RB,0 in and T0 in K using (6). 36th International Physics Olympiad. Salamanca (Espaa) 2005 Exp. Page 5 of 11 R.S.E.F. OPT

26、ICAL PROPERTIES OF THE FILTER The liquid filter in the test tube is an aqueous solution of copper sulphate (II) and Orange (II) aniline dye. The purpose of the salt is to absorb the infrared radiation emitted by the filament. The filter transmittance (transmitted intensity/incident intensity) is sho

27、wn in Figure F-6 versus the wavelength. 0 5 10 15 20 25 30 450500550600650700750 /nm % transmittance F-6 Task 3 Determine 0 and from Fig. F-6. Note: 2 is the total width at half height and 0 the wavelength at the maximum. 36th International Physics Olympiad. Salamanca (Espaa) 2005 Exp. Page 6 of 11

28、R.S.E.F. PROPERTIES OF THE LDR The material which composes the LDR is non conducting in darkness conditions. By illuminating it some charge carriers are activated allowing some flow of electric current through it. In terms of the resistance of the LDR one can write the following relation = bER (7) w

29、here b is a constant that depends on the composition and geometry of the LDR and is a dimensionless parameter that measures the variation of the resistance with the illumination E produced by the incident radiation. Theoretically, an ideal LDR would have = 1, however many factors intervene, so that

30、in the real case 9.5 V, wait 10 min approximately before making the first reading. Then wait 5 min for the second one, and so on. Before doing any further calculation go to next step. b) Once obtained the lowest value of the resistance R, open the protecting cover, put the grey filter as indicated i

31、n F-9, cover again - as soon as possible - the platform and record the new LDR resistance R. Using these data in (8) compute and . c) Modify Eq. (3) to display a linear dependence of ln R on 0.83 B R. Write down that equation there and label it as (9). d) Using now the data from a), work out a table

32、 that will serve to plot Eq. (9). e) Make the graphics plot and, knowing that c2 = hc/k, compute h and h by any method (you are allowed to use statistical functions of the calculators provided by the organization). (Speed of light, c = 2.998 108 m s-1 ; Boltzmann constant, k = 1.38110-23 J K-1) F F-

33、8 F-9 F-7 36th International Physics Olympiad. Salamanca (Espaa) 2005 Exp. Page 7 of 11 R.S.E.F. 36th International Physics Olympiad. Salamanca. Spain. Experimental Competition, 7 July 2005 COUNTRY NUMBER COUNTRY CODE STUDENT NUMBER PAGE NUMBER TOTAL No OF PAGES Answer sheet 1 TASK 1 (2.0 points) Dr

34、aw the electric connections in the boxes and between boxes below. Pm B V A P Photoresistor Incandescent Bulb Potentiometer Red socket Black socket Ohmmeter Voltmeter V Ammeter A Platform P Potentiometer Pm Battery B 36th International Physics Olympiad. Salamanca (Espaa) 2005 Exp. Page 8 of 11 R.S.E.F. 36th International Physics Olympiad. Salamanca. Spain. Experimental Competition, 7 July 2005 COUNTRY NUMBER COUNTRY CODE STUDENT NUMBER PAGE NUMBER TOTAL No OF PAGES Answer sheet 2 TASK