物理实验报告(英文)

物理实验报告(英文)
Introduction
The Planck constant is a constant of physics which reflects the magnitude of energy quantum in the field of quantum mechanics. The sign of Planck constant is h and it is named by Max Planck in 1990. The proportionality constant between a photon’s energy and the frequency of its electromagnetic wave was the first definition of the Planck constant. This theory was generalized by Louis de Broglie in 1923 and confirmed by experiments. There is a difference between h and (h-bar). is called the Dirac constant or reduced Planck constant which is equal to the Planck constant divided by 2π.(1)The photoelectric effect is the effect that when a matter which can be metals, non-metallic solids, liquids or gases is bombarded by photons (light), electrons in the substance will absorb the energy of photons and they will be emitted, one electron could only absorb the energy of one photon. It is usually a way to find the Planck constant. As the limiting of the facilities, the main results which include the wavelength of lights and the planck constant are not easy to be gotten in accurate values. This lab was designed to find the Planck constant based on the light diffraction and the photoelectric effect, there are four aims of this experiment which are building a spectrometer, finding wavelengths for lasers and LEDS and finding the Planck constant.
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Theorem
When a beam of monochromatic light passing through a diffraction grating, the wavelength and the distance from the grating to the center
relationships, n is the order of fringes and it is equal to ⋅⋅⋅⋅⋅⋅3,2,1,o , λ is the wavelength of this light, L , y , d are the distance from the grating to the center fringe, the fringes to the center fringe and the distance between two slits in the grating respectively, θ is the angle between the center line and the line connected by the fringe center and the slit. The formula of the photoelectric effect is w hf E -=, E is the energy of the electro escaping from the object, f is the frequency of the light which shots at the surface of the object, h is the Planck constant and w is the work function. For a certain object, the work function is a constant. For LED, This formula also can be rewritten as w hf eV -= where e is the quantity of electric charge and it is c 19106.1-⨯and V is the voltage of the LED. For EM wave, f C CT =
=λ(C is the speed of light and f is its frequency.
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Formula :θλsin d n =, )(tan 1L y -=ϑ, w hf E -=, w hf eV -=, f
C CT ==λ.
Aims
Aim I : building a spectrometer
● Apparatus: carton, circular diffraction grating, a piece of paper, ruler, white light LED, scissors.
Diagram 1 is the simple model the spectrometer
● Diagram 1: simple model of the spectrometer
● Methods
The process of making a simple spectrometer was mainly 5 steps and operated by two people. First of all, a hole with proper sizes in the front of the carton was removed by the scissors. Secondly, a circular diffraction grating was set to the hole to cover it, which was used to produce the diffraction pattern. Thirdly, a piece of paper was fixed at the internal back surface of the carton, which was served as a screen to bring out the diffraction pattern. Then, at a proper position on the top surface, an elliptic hole which was long and narrow (this is to help to view because the light from THE LED is not be very strong) was removed to view the diffraction pattern which was inside the carton. Next, a ruler was put at the bottom near to the back surface and the purpose of this step was measuring the distance between different fringes.
The experiment started after the spectrometer was finished. At the first, the light of the torch was shot to the center of the diffraction grating vertically and the diffraction pattern appeared on the screen. Then, observing the diffraction pattern through the viewing hole in top and record the position of each fringe. Next, the distances from the center to each fringe were read from the ruler and they are recorded on the drafter paper. Later, the length (L) between the front surface and the back surface was measured and recorded. At last, the result was recognized into the table which was on the tutorial.
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Result
i. Problems with building and using the spectrometer
During the process of building and using the spectrometer, there are some problems existing and which will lead to errors of the experiment result. When the spectrometer was made, the carton was not perfect cube, so the length (L) between the front surface and the back surface is not accurate. With the change of fringes, L is not a certain value and it will change, this is because sides of the nonstandard cube are not parallel to each other respectively. The hole with diffraction was hard to be put at the center of the front surface as the position was estimated by eyes. The positions of each fringe were recorded while the brightest fringe at the center of the back surface, so the brightest fringe is not vertical to the screen and which will lead to the distances between the fringes and the center fringe were not correct. While operating this experiment, the viewing hole in the top is narrow, so the position of each fringe cannot be labeled correctly. Due to the weakness of the light and seven different monochromatic lights gathering together, it is not easy to tell where is the fringe center of each monochromatic light and which also will cause the errors on marking the positions.
ii. Results table
Table 1 shows the experiment data of aim 1 and the wavelengths of
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7 different monochromatic lights calculated from the it.
Table 1: results of aim 1.
As shown in table1, the wavelengths of the red light, yellow light, green light and the blue light are 643.6 nm, 548.9 nm, 482.3 nm and 377.5 nm respectively. So from the red light to the blue light, their wavelengths are deduced. After the white light shots at the diffracting grating, there are light
and dark sections alternating with each other. Three fringe fields which are in light sections appear on the screen and they are symmetry with the center fringe. In each fringe field, there are red, orange, yellow green, blue, indigo and violet from the right side to the left side respectively.
Analysis
The wavelength of the red, yellow, green and blue light is 643.6nm, 548.9 nm, 482.3 nm, 377.5 nm respectively. The formulas are θλsin d n = and center fringe to the slits is m 215.0. The total length of the diffraction grating is mm 1with 600 slits, so the distance (d ) between to slits is
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different value of y, the wavelength of each monochromatic light was gotten and they are shown in table 1. Table 2 below is the comparison of the standard wavelength for the for lights.
Table 2 is the comparison between the standard wavelength and the wavelength gotten from this experiment of the four monochromatic lights.
Table 2: comparison
According to this table, only the wavelength of red light is in the range of the standard wavelength. The wavelengths of the yellow, green, blue light gotten from aim 1 are smaller than the real value, which are caused by the errors discussed before. Therefore, the results are not very accurate. Monochromatic light is the kind of light that has a single wavelength (2). The light comes from the torch is White light. White light is composed of seven lights which are red, orange, yellow…… and it has seven wavelengths (3). Therefore, white light is polychromatic light and this is the reason why the diffracting pattern has different colors. Light is a kind of EM wave. EM wave has visible spectrum and the invisible spectrum. When the frequency of light is between HZ 14103.4 and
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HZ 14105.7 , it is visible light which includes red, orange, yellow, green, blue, indigo, violet light. When the frequency of light is out of this range, it is invisible light (4).
● Apparatus: spectrometer, a piece of paper, ruler, red laser pen, blue laser pen, red and blue goggles.
● Methods
Goggle is a kind of light filter and it can avoid the light damaging to the eyes by
changing the intensity and spectrum of the through lights. The ways of this aim is similar to the aim 1. First of all, one person used the red laser pen to shot at the diffraction grating and the other person observed the diffraction pattern by wearing a blue goggle. The reason why blue goggle was used to observe the red laser is that it can absorb the red light which will protect the eyes , in the same way, the red goggle was put on to protect the eyes when the blue laser pen was used (5). Then, the position of each fringe was recorded. Next, the distance from the different fringes to the center fringe was read from the ruler and it was recorded at another sheet of paper. Later, using the blue laser pen and wearing the red goggle to repeat the last steps.
●Results
Table 3 shows the experiment data of aim 2 and the wavelength of the red and blue laser gotten from it.
Table 3: results of aim 2
The wavelength calculated from the second order is smaller than the first order, which can be seen from table 3. Both diffraction patterns of the red laser and blue laser have five bright sections and they symmetry about the center fringe. The bright section and the dark section are alternating with each other. When the bright section got far from the center fringe, it became darker and darker. So the brightness of second order is darker than the first order.
●Analysis
Table 4 shows the wavelength of the red light and the blue light from aim 1 and aim 2
Table 4: Comparison of the results for aim 1 and aim 2
Two fringe orders of diffraction could be seen in aim 2 and there is a
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fringe on the sides as well as the back (6). The wavelengths of the red and blue LED calculated from the first order are 618.9 nm and 405.9 nm. From the second order, the wavelengths are 607.5 nm and 393.0 nm respectively. The results of the two aims are not the same: wavelengths of the red light in aim 2 for the first and second order are smaller than aim 1 while which of the blue light of aim 2 are bigger than aim 1 (8). The values of wavelengths of different orders in aim 2 are different. As the pattern of the first order is brighter than the second order, when marked the position of fringes, it will be more accurate. Thus, the result gotten from the first fringe will be more accurate than the second order and they are different. The different separations also will lead to the different results. If the slit separation becomes narrower, the diffraction pattern will become clearer. On the opposite side, the pattern will become unclear when the slits separation is wider (7).
●Apparatus:
Spectrometer, LEDs, power supply, black plastic bag, leads.
●Methods
i. Connect the powers supply and the socket and let the voltage is the
minimum value
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ii. Connect the Red LED to the power supply and regulate the voltage at
a proper value to make the LED shine normally.
iii. Let the light of the red LED pass through the empty pen and shot at the spectrometer through the diffraction grating. The diffraction pattern will be more clear when the LED passed through the empty pen as the light was gathered and its intensity was strengthened (9).
iv. Observe the diffraction pattern from the viewing hole with the black plastic bag covered the head and the viewing hole (the LED was not bright and not easy to be seen, to reduce the light loss and help view, the black plastic bag was used).
v. Take done the position of the center of each fringe.
vi. Read the distance from each fringe to the center fringe
vii. Recognize the result and move it to the table in tutorial
viii. U sing the yellow, blue and green LEDs respectively to repeat the above process
Results
Table 5 shows the experiment data of aim 3 and the wavelength, frequency of the four LEDs gotten from the result.
Tabl e 5: results of aim 3
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The phenomenon of this aim is not very clear to see, there are three bright circular sections. In each section, the brightness became smaller and smaller from the center to the sides. Of the four color LEDs, the blue LED is brightest, then are the green, yellow, red LED respectively. This was seen from the experiment.
Analysis
The wavelength was gotten from the same way of calculation as aim1. f
C CT ==λλC f =⇒()/1038s m C ⨯=, so the frequency of each LE
D can be calculated. The wavelength of the red LED, yellow LED, green LED, blue LED from this aim are nm 662, nm 594, nm 555 and nm 482respectively. The frequencies of them are Hz 14105.4⨯,Hz 141005.5⨯,Hz 141040.5⨯ and
Hz 141022.6⨯.
Table 6 shows the comparison between the wavelengths, frequencies of the four LEDS gotten of aim 3 and the standard value
Table 6: comparison
As shown in table 6, both the wavelengths and the frequencies of the red LED, yellow LED and green LED are in the range of the standard value. However, the result of the blue LED was out of the range. This aim works well and the results are more accurate than the previous aims.
●Apparatus
Spectrometer, LEDs, power supply, black plastic bag, leads.
●Methods
i. Connect the powers supply and the socket and let the voltage is the
minimum value.
ii. Connect the red LED to the power supply.
iii. Regulate the value of voltage through the power supply and make it increase slowly.
iv. When the LED just started to shine, writing done the voltage V, stopping to regulate the voltage and using the LED to shot the diffraction grating.
v. Viewing the diffraction pattern on the screen through the viewing hole with the black plastic bag covered the head and the hole.
vi. Mark the position of the center of each fringe on the screen paper. vii. Read the distances from each fringe to the center fringe and write the
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data onto another sheet of paper.
viii. R eplace the red LED into yellow LED, blue LED and green LED respectively and repeat the above process for each of them.
ix. Using the data to draw a graph of eV on Y against f on x.
Result
Table 7 shows the experiment data of aim 3 and the wavelength, frequency of the four LEDs gotten from the result.
Tabl e 7: results of aim 3
The frequencies were calculated from the same method as aim 3. On the screen, the diffraction pattern of the red LED was not clear and the pattern of the blue LED is brightest. The pattern of the green LED was more clear than the tallow LED and the red LED. For each LED, the patterns were similar to each other and they had three bright sections, the brightness was reduced from the center of the bright fringe to its edge in every bight section. In this table, eV is energy of the
V
photoelectron escaping from the LED,
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Is the value of voltage when the LED started to shine and h is the Planck constant.
Graph 1 is the relationship between eV and the frequency of the light. Graph 1: the relationship between eV and frequency.
For this graph, x-axis is the frequencies of different kinds of light, y-axis is energy of the photoelectron.
Analysis
The equation of eV against frequency is w hf eV -=, w is work function. For the equation, the gradient is the Planck constant, and the intercept is the work function. According to graph1, the equation of the relationship between eV and frequency is 259.1819.0-=x y , as the unit magnitude of the x-axis is Hz 1410and it of the y-axis is J 1910-. So
s J h ⋅⨯=⨯=--341419
1019.810
10819.0. The real value of the Planck constant
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is s J ⋅⨯-341063.6, so the result is not very accurate. There exist some errors. First of all, as the weakness of the LEDs and eyes cannot tell the fringes center accurately, the distance (y) from fringes to the center fringe is not accurate and it will lead to the inaccuracy of frequency. Secondly, the voltage used should be the instant voltage while the LED was just starting to shine. However, this is impossible to achieve. The above two errors are the largest causes of errors. The distance (L) between the grating to the center fringe is also not accurate as it read by eyes, which is the third error. Therefore, errors on reading the distance and the voltage are two approximate measurement errors (10). In addition, the uncertain errors also exist. The LED may shine abnormally as it was used before or some other internal problems are in the LED, this may is an error and it is uncertain..Operating this experiment in the dark, using the new LEDs and using other materials which are more stable instead of carton are three measurements can be done to improve the accuracy of this experiment (10). The answers from the LED with two colors cannot be used to find h as it is not monochromatic light and it has two frequencies (11). The error in the method for finding h can be calculated by this method which is Js s h h 3410)(-⨯±=, where s is the corrected standard deviation. ∑--=n i i h h n s 2)(11.The Planck
constant s J h ⋅⨯=-341063.6, Four colors of light were measured, so 4=n .
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From table 7,1h , 2h ,3h ,4h are Js 3410942.4-⨯, Js 3410018.6-⨯,
Js 3410221.6-⨯and Js 3410916.5-⨯respectively. So
⇒⨯=+++=-3443211066175.54
h h h h h ⇒⨯-=--=∑∑-412342)1066175.5(3
1)(11hi h h n s n i i ()[]24232221)()()(31h h h h h h h h s -+-+-+-=
. Substituting them and s can be worked out which is 341006.1-⨯. Therefore,Js h 34343410)1006.11066175.5(---⨯⨯±⨯=(12).according to the website which is called Investopedia (2012), the standard deviation stands for the rate of deviation between the stochastic variable and the mathematic expectation, so a low s means that the result s were close together. The standard deviation of the result gotten from aim 4 is 341006.1-⨯from the real h. as the errors of the results have no regular pattern, the errors are random, not systematic(12).
Conclusion
This lab has finished 4 aims which are building a spectrometer, finding wavelengths for lasers and LEDS and finding the Planck constant, the Planck constant was also gotten from the experiment based on the light diffraction and the photoelectric effect. To sum up, the spectrometer used to measure wavelengths is useful as it can produces the diffraction
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pattern and shows the pattern on the screen. Also, the distance from the fringes to the center fringe can be read from the bottom ’s ruler directly as well as the distance from the center fringe to the grating. The spectrometer is easy to be made and operated. However, due to the unstable property, the data must be read from the viewing hole and the light will lose from it, the spectrometer is not very accurate. From Wikipedia, there is another way to measure the Planck constant which is Watt balance method. The Watt balance is a tool to compare two powers, one of which is measured in conventional electrical units and the other is in SI watts. According to the explanation of the conventional watt, K J R K 2 with SI unit can be measured where K R is the Von Klitzing constant and it can be measured from the effect of quantum Hall. In the particular situation 2/e h R K =can be assumed, thus, the Planck constant
with the photoelectric effect, the watt balance method to measure the Planck constant is hard to be operated and it only can work in the particular situation, in addition, the result gotten from this method also not very accurate. Therefore, the photoelectric effect is better and easier than the watt balance method to measure the Planck constant.
Reference :
Investopedia (2012) Standard deviation [Internet], Available from:
<> [Accessed 15th May 2012].
Wikipedia (2012) Watt balance [Internet], Available from:
<e > [Accessed 15th May 2012].
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