The Photoelectric Effect Essay, Research Paper
The Photoelectric Effect
The intent of this experiment is to find h/e ( Plank & # 8217 ; s invariable in units of negatron Vs ) , the work map F, and the threshold frequence for the photochathode surface provided.
Three filters each holding a distinguishable wavelength, were used to transport out this experiment. Using these filters, 435.8 nanometer, 546.0 nanometer, and 577.0 nanometer, informations in electromotive force and current was collected, as potency was selected at random points for each wavelength. This information was so plotted ( current vs. potency ) , and halting potency was determined. Stoping possible for: 435.8 nanometer is 1.52 V, 546.0 nanometer is 1.17 V, and
577.0 nanometer is 0.8 V. This information was so used to cipher frequence for each wavelength using the equation degree Fahrenheit = c/l. Frequency information was plotted against halting possible as mentioned above to find Plank & # 8217 ; s constant, h/e = 3.62 * 10-15 eV*s, besides work map, F = 1 V, and threshold frequence, fo = 2.7 * 1014 Hz. Under 12 % mistake is found when compared to the theoretical value ( h/e = 4.14 * 10-15 eV*s ) for Plank & # 8217 ; s invariable. This can be a consequence from the graph, because the best fitting additive line is supposed to be provided in order to cipher Planck & # 8217 ; s invariable. This has to be really accurate, and the best line was chosen to minimise mistake.
If frequence of visible radiation is increased, the maximal KE of the negatrons increases linearly, that is KEmax = hf & # 8211 ; F. If the frequence, degree Fahrenheit, is less than the & # 8220 ; cutoff & # 8221 ; frequence, field-grade officer, where hfo = F, no negatrons will be emitted.
Introduction
The photoelectric consequence refers to the fact that when light radiances in a metal surface, negatrons are emitted from the surface. The photoelectric consequence occurs in other stuffs besides, but most apparent with metals. It is said that negatrons should be emitted when light radiances on a metal surface is consistent with the electromagnetic moving ridge theory of visible radiation, since the electric field of the electromagnetic moving ridge could exercise a force on negatrons in the metal and thrust some of them out. Einstein pointed out, that the moving ridge theory and the photon theory of visible radiation could give really different anticipations on the item of the consequence. Analyzing the moving ridge theory against Einstein & # 8217 ; s atom theory. The two of import belongingss of a light moving ridge are its strength and its frequence ( or wavelengths ) . When these two measures are varied, the moving ridge theory makes theses following anticipations. If light strength is increased, the figure of negatrons ejected and their maximal KE should be increased because the higher the strength means greater electric field amplitude and the greater the electric field should thrust negatrons at a higher velocity. Besides, the frequence of the visible radiation should non consequence the KE of the negatrons. Merely the strength should impact the KE. Make these anticipation stand correct for this type of consequence? Is at that place another type of theory that will stand rectify? This will be discussed in the study after the experiment.
The intent of this experiment is to find h/e ( Plank & # 8217 ; s invariable in units of negatron Vs ) , the work map F, and the threshold frequence for the photochathode surface provided. A proper setup has been provided for this experiment and the observations are as follows in the study.
Theory
A metal home base along with a smaller electrode is placed inside an evacuated glass tubing, called a photoelectric cell. The two electrodes are connected with an ammeter, voltmeter and a beginning of voltage. When the photoelectric cell is in the dark, the ammeter reads nothing. When visible radiation of sufficiently high frequence is shone on the home base, the ammeter shows current fluxing in the circiut. Look at figure 1, to understand the completion of the circuit, to conceive of the negatrons fluxing across the tubing from the home base to the & # 8216 ; aggregator & # 8217 ; . From this apparatus the maximal kinetic energy ( KEmax ) can be measured from the emitted negatrons. This can be done by a variable electromotive force beginning and change by reversaling the terminuss so that the aggregator electrode is negative and the home base electrode ( metal ) is positive. The negative electrode will drive the negatrons emitted from the home base. If the reversed electromotive force is increased, there is a point where the ammeter reads zero, or no negatrons have been emitted. This is called the & # 8220 ; halting possible & # 8221 ; Vo, from the measurings KEmax can be determined from:
KEmax = eVo = hf & # 8211 ; F
Where H is Plank & # 8217 ; s constant, degree Fahrenheit is the frequence of visible radiation, vitamin E is the electronic charge, and F is the work map of the cathode surface. Since the negatrons are held in the metal by attractive forces, a minimal energy, F, called the work map, is required to let go of the negatron from the electrode surface. If the frequence degree Fahrenheit, of the entrance visible radiation is so low that hafnium F, so negatrons will be emitted and energy will be conserved at the same clip. That is, the input energy ( of the photon ) , hf, should be the KE of the negatron plus the energy required to acquire it ejected from the metal electrode, F:
hafnium = KE + F ( photoelectric equation )
Apparatus
This is called the Plank & # 8217 ; s changeless setup, and has been designed to find the magnitude of a cardinal physical measure, Plank & # 8217 ; s invariable. It consists of a phototube in which where the photoelectric emanations occurs, two variable resistors for seting the electromotive force to a all right degree. A card incorporating three distinguishable filters which is placed in forepart of the phototube. The filters are placed in the manner of the quicksilver visible radiation and are numbered harmonizing to wavelength. The three filters used in the setup are: 577.0 nanometer, 546.0 nanometer, and 435.8 nanometer. As seen
in the diagram there consists a voltmeter and an ammeter. The ammeter stands as an electrometer, which measures the sum of negatrons ejected. The voltmeter measures the potency to find the halting potency.
Procedure
First, linking the battery ( voltage ) completed the circuit, and so the quicksilver visible radiation was turned on. We made certain that we didn & # 8217 ; t look straight into the quicksilver visible radiation, due to harmful ultraviolet beams. Then, the retarding potency was set at its lower limit utilizing the coarse and all right electromotive force adjustors on the phototube unit. Potential was measured by the voltmeter provided. The lamp was so set in forepart of the phototube get downing with the 435.8 nm filter and the spacing was adjusted until the ammeter read about
0.4 * 10-6 A. Measurements for photocurrent were taken as electromotive force was retarding. Most of the information was taken at the part where the current & # 8217 ; saturates & # 8217 ; so that accurate finding of halting possible can be made. All of the above was so repeated for the other two filters, and all informations was recorded.
During the experiment, a current versus electromotive force graph was plotted in order to roll up informations at the impregnation points and find the halting possible for each wavelength accurately. When all information was collected the quicksilver visible radiation was turned off and the circuit was dissembled.
After the experiment was complete, a graph of halting possible versus frequence was constructed. The incline of this additive graph was calculated in order to happen h/e ( Plank & # 8217 ; s invariable in units of negatron Vs ) . The interception of the line with the halting possible axis will find the work map F. Interception of the line with the frequence axis will give us the cutoff frequence field-grade officer.
Consequences
Goal: To happen stopping possible for different frequences. Voltage was indiscriminately selected in order to find the halting possible for each wavelength. These values were so plotted in a current ( I ) versus electromotive force ( V ) graph to find the halting possible for each wavelength. The consequences are as follows in the undermentioned tabular arraies for each wavelength.
Table 1:
Wavelength ( cubic decimeter ) = 435.8 nanometer
Current I ( A nanometer ) Voltage ( V )
-22.0 3.15
-22.0 1.517
0.0 0.922
55.0 0.138
17.0 1.33
Stoping possible ( Vo ) = 1.52 V
Expression at graph 1.
Table 2:
Wavelength ( cubic decimeter ) = 546.0 nanometer
Current I ( A nanometer ) Voltage ( V )
-20.0 3.16
-20.0 1.17
30.0 0.138
0 0.66
0 0
Stoping possible ( Vo ) = 1.17 V
Expression at graph 2.
Table 3:
Wavelength ( cubic decimeter ) = 577.0 nanometer
Current I ( A nanometer ) Voltage ( V )
-10.0 3.16
-10.0 0.8
0 0.655
30.0 0.138
-15.0 1
Stoping possible ( Vo ) = 0.8 V
Expression at graph 3.
Goal: To happen Plank & # 8217 ; s invariable from the mentioned informations. From the old graphs, the halting potency was determined for each wavelength. Frequency was calculated for each wavelength. Using this information another graph was constructed in order to find Plank & # 8217 ; s invariable. Stoping possible ( Vo ) versus frequence ( degree Fahrenheit ) was plotted utilizing the following informations in table 4.
Table 4:
Wavelength cubic decimeter ( nm ) Stoping possible Vo ( V ) frequence degree Fahrenheit ( Hz * 1014 )
435.8 1.52 6.9
546.0 1.17 5.5
577.0 0.8 5.2
Expression at graph 4.
From this graph the incline was calculated to be h/e = 3.62 * 10-15 eV*s, which is Plank & # 8217 ; s invariable. This is under 12 % from the theoretical value ( 4.14 * 10-15 eV*s ) . Besides the followers was besides determined from the graph:
Table 5:
h/e ( eV*s ) Work Function F ( V ) Threshold Frequency field-grade officer
( Hz * 1014 )
3.62 * 10-15 1.0 2.7
An illustration of each computation is provided in the appendix.
Mistakes
Under 12 % mistake is found when Plank & # 8217 ; s invariable is compared to the theoretical value ( h/e = 4.14 * 10-15 eV*s ) . This can be a consequence from the graph, because the best fitting additive line is supposed to be provided in order to cipher Planck & # 8217 ; s changeless utilizing the incline of the graph. This has to be really accurate, and the best additive line was chosen in this instance to minimise mistake.
Another factor includes, the equipment used. An ammeter and a voltmeter were used invariably in entering informations. These devices might non every bit accurate as they seem. It is possible that opposition is present it the devices or in the wires linking them together hence, incorrect informations could hold been collected. This could impact informations in halting possible. More accurate devices equal more accurate consequences. New and higher quality devices might non hold every bit much internal opposition, which would assist.
Decision
An addition in strength of the light beam means more photons are incident, so more negatrons will be ejected ; but since the energy of each photon is non changed, the maximal KE is non changed. If frequence of visible radiation is increased, the maximal KE of the negatrons increases linearly, that is KEmax = hf & # 8211 ; F. If the frequence, degree Fahrenheit, is less than the & # 8220 ; cutoff & # 8221 ; frequence, field-grade officer, where hfo = F, no negatrons will be emitted. These are anticipations of the photon theory and are clearly different of the anticipations of the moving ridge theory that were mentioned in the debut. These consequences harmonizing to the photoelectric consequence are in understanding with Einstein & # 8217 ; s photon theory.
