Wednesday, June 12, 2013
Wednesday, May 29, 2013
Color and Spectra
Objective
The purpose of this experiment was to determine the relationship function between theoretical and measured wavelength and use this function to the different between thewavelength of a hydrogen gas spectra
Experiment
white light source
The purpose of this experiment was to determine the relationship function between theoretical and measured wavelength and use this function to the different between thewavelength of a hydrogen gas spectra
Experiment
white light source
Spectra observed through a diffraction grating
measurements and calculation of wavelengths
derivation of λ = Dd/√(L2+D2)
a calibration function was determined.
spectra of a hygrogen gas
calculating experimental wavelengths
calibrated wavelengths vs. theoretical wavelengths
Experimental calibrated wavelength (nm)
|
Theoretical wavelength (nm)
|
423±25
|
410
|
490±14
|
486
|
680±27
|
656
|
Conclusion
The expeiment was succeed. All the results are within the uncertainty.
Measuring a human hair
Purpose
The purpose of this experiment was to measure the human's hair. We using Young's double slits experiment.
Experiment
Setting up the equipment:
A laser which produces light rays of around 650 nm wavelength was used in this experiment, and the interference image was projected on a white board.
The length of a slit on the edge was recorded.
Measure the thickness of a hair with a micrometer
Conclusion
This experiment was successfully finished. The result has an error of 22.6% which is good.We learned how to use Young's double slits to measure a object thickness.
Setting up the equipment:
 |
A laser which produces light rays of around 650 nm wavelength was used in this experiment, and the interference image was projected on a white board.
The length of a slit on the edge was recorded.
Measure the thickness of a hair with a micrometer
Data and Analysis
Wavelength,λ (nm)
|
633
|
Distance,L (cm)
|
150 ± 1
|
Distance between 2 fringes,y (mm)
|
11.906 ± 0.01
|
Experimental diameter of the hair (μm)
|
79.7 ± 0.65
|
Actual Diameter of the hair (μm)
|
65 ± 10
|
% error (%)
|
22.6
|
Conclusion
This experiment was successfully finished. The result has an error of 22.6% which is good.We learned how to use Young's double slits to measure a object thickness.
Tuesday, May 28, 2013
Determine the Plank's Constant
Objective
In this experiment, we will view the spectrum of colors found in white light and measure the wavelength of several different colors
Set up the LED and rulers
In this experiment, we will view the spectrum of colors found in white light and measure the wavelength of several different colors
Experiment
Measure the length of color from each LEDs
 |
| Use the mutimeter to measure the voltage across the LEDs and multiply by (e-) to get the energy |
Datas and results
Conclusion
In this experiment, we measured the wavelengths of the diffraction lights. And we graph the E vs c/lambda. The slope of the graph should be the Plank's constant and our error is about 15% which is acceptable.
Classical Harmonic Oscillator
Objective
The purpose of this experiment was to study quantum mechanics in classical harmonic oscillator with a simulation.
Experiment
Potential Energy Diagrams
Experiment
Potential Energy Diagrams
Potential energy diagram
1&2.The range of motion is from -5cm to 5cm because the energy the particle is bigger than well in this region.
3. The more time the particle spends in one region, the more likely it is to be detected in that region. The particle spends more time to the left of zero because its kinetic energy (and hence its speed) is much smaller in that region. Therefore, the particle is much more likely to be detected to the left of zero.
4. The turning points move outward from the origin by a factor of the square root of two because 1/2 kx^2 = U
5. The shape of the kinetic energy is a parabola, with the opending down.
6. At the turning point. Because the kinetic energy of the particle at the turning points are zero, it is easier to be detected.
Potential Well
1.
E = n2 h2 / 8 m L2
= (1)2 (6.626 x 10-34 J s)2 / 8 (1.673 x 10-27 kg) (10 x 10-15 m)2E = 3.3 x 10-13 J
= 2.1 MeV
No, it is different from finite well.
2.
E = n2 h2 / 8 m L2
= 4 (2.1 MeV)
= 8.4 MeV
No, it is not the energy of the first excited state from finite well.
3. The wavelength of the wavefunction is larger in the finite well than infinite well, because the wavefunction can penetrate into the "forbidden" regions.
1&2.The range of motion is from -5cm to 5cm because the energy the particle is bigger than well in this region.
3. The more time the particle spends in one region, the more likely it is to be detected in that region. The particle spends more time to the left of zero because its kinetic energy (and hence its speed) is much smaller in that region. Therefore, the particle is much more likely to be detected to the left of zero.
4. The turning points move outward from the origin by a factor of the square root of two because 1/2 kx^2 = U
5. The shape of the kinetic energy is a parabola, with the opending down.
6. At the turning point. Because the kinetic energy of the particle at the turning points are zero, it is easier to be detected.
Potential Well
1.
E = n2 h2 / 8 m L2
= (1)2 (6.626 x 10-34 J s)2 / 8 (1.673 x 10-27 kg) (10 x 10-15 m)2E = 3.3 x 10-13 J
= 2.1 MeV
No, it is different from finite well.
2.
E = n2 h2 / 8 m L2
= 4 (2.1 MeV)
= 8.4 MeV
No, it is not the energy of the first excited state from finite well.
3. The wavelength of the wavefunction is larger in the finite well than infinite well, because the wavefunction can penetrate into the "forbidden" regions.
4. The energy will decrease. The wavelength of the wavefunction is larger in the finite well than infinite well, so on the same state, the energy of finite well is smaller than infinite well. It shows that as the depth of the well decreases, the energy decreases.
5. The penatrate depth will decrease. As the mass of the particle increases, the chance to penentrate through the forbidden region decreases. Finally, when it is up to a large enough mass, it is consistent with the classical harmonic oscillator in macro scale.
5. The penatrate depth will decrease. As the mass of the particle increases, the chance to penentrate through the forbidden region decreases. Finally, when it is up to a large enough mass, it is consistent with the classical harmonic oscillator in macro scale.
Relativity
Objective
The purpose of this experiment was to study the changing of time and length under the special theory of relativity.
Time Delay
Question 1: Distance traveled by the light pulse
How does the distance traveled by the light pulse on the moving light clock compare to the distance traveled by the light pulse on the stationary light clock?
1. The distance traveled by the light pulse on the moving light clock is longer than the distance traveled by the light pulse on the stationary light clock.
Length Contration
Question 1: Round-trip time interval, as measured on the light clock
Imagine riding on the left end of the light clock. A pulse of light departs the left end, travels to the right end, reflects, and returns to the left end of the light clock. Does your measurement of this round-trip time interval depend on whether the light clock is moving or stationary relative to the earth?
1. The measurement of this round-trip time interval depend on whether the light clock is moving or stationary relative to the earth.
Question 3: Why does the moving light clock shrink?
You have probably noticed that the length of the moving light clock is smaller than the length of the stationary light clock. Could the round-trip time interval as measured on the earth be equal to the product of the Lorentz factor and the proper time interval if the moving light clock were the same size as the stationary light clock?
3. In order for the time intervals to obey this law, the length of the moving light clock had to be made smaller.
Question 4: The length contraction formula
A light clock is 1000 m long when measured at rest. How long would earth-bound observer's measure the clock to be if it had a Lorentz factor of 1.3 relative to the earth?
4. Lp = 1000m, γ =1.3. L=?
L= Lp/γ = 769m
The purpose of this experiment was to study the changing of time and length under the special theory of relativity.
Time Delay
Question 1: Distance traveled by the light pulse
How does the distance traveled by the light pulse on the moving light clock compare to the distance traveled by the light pulse on the stationary light clock?
1. The distance traveled by the light pulse on the moving light clock is longer than the distance traveled by the light pulse on the stationary light clock.
Question 2:
Time interval required for light pulse travel, as measured on the earth
Given that the speed of the light pulse is independent of the speed of the light clock, how does the time interval for the light pulse to travel to the top mirror and back on the moving light clock compare to on the stationary light clock?
Given that the speed of the light pulse is independent of the speed of the light clock, how does the time interval for the light pulse to travel to the top mirror and back on the moving light clock compare to on the stationary light clock?
2. The time interval for the light pulse to travel to the top mirror and back on the moving light clock is longer than the interval on the stationary light clock because the distance is longer in the moving clock and speed of light is constant.
Question 3: Time interval required for light pulse travel, as measured on the light clock
Imagine yourself riding on the light clock. In your frame of reference, does the light pulse travel a larger distance when the clock is moving, and hence require a larger time interval to complete a single round trip? Run the simulation, which this time displays timers at rest on both the light clock and the earth.
Imagine yourself riding on the light clock. In your frame of reference, does the light pulse travel a larger distance when the clock is moving, and hence require a larger time interval to complete a single round trip? Run the simulation, which this time displays timers at rest on both the light clock and the earth.
3. The light pulse travel a larger distance when the clock is moving, and hence require a larger time interval to complete a single round trip. The minimum time interval between events is referred to as the proper time.
Question 4: The effect of velocity on time dilation
Will the difference in light pulse travel time between the earth's timers and the light clock's timers increase, decrease, or stay the same as the velocity of the light clock is decreased?
Will the difference in light pulse travel time between the earth's timers and the light clock's timers increase, decrease, or stay the same as the velocity of the light clock is decreased?
4. As the speed of the light clock is reduced, the difference between the distance traveled by the light pulse and the distance between the mirrors decreases. As this distance difference decreases, the time difference also decreases. Comparing the images below and above, the time difference decreases as the gamma value decreases. When gamma value decreases, the velocity of the traveling light clock decreases, and the time difference decreases.
5. Using the time dilation formula, predict how long it will take for the light pulse to travel back and forth between mirrors, as measured by an earth-bound observer, when the light clock has a Lorentz factor (γ) of 1.2.
Δt = γΔtproper = 1.2(6.67 µs) = 8.004 µs predicted
actual Δt= 8.00µs very close to the predicted, 8.004s.
6. If the time interval between departure and return of the light pulse is measured to be 7.45 µs by an earth-bound observer, what is the Lorentz factor of the light clock as it moves relative to the earth?
Δt = γΔtproper
Δt = 7.45 µs; Δtproper = 6.67 µs
γ =1.12
Length Contration
Question 1: Round-trip time interval, as measured on the light clock
Imagine riding on the left end of the light clock. A pulse of light departs the left end, travels to the right end, reflects, and returns to the left end of the light clock. Does your measurement of this round-trip time interval depend on whether the light clock is moving or stationary relative to the earth?
1. The measurement of this round-trip time interval depend on whether the light clock is moving or stationary relative to the earth.
Question 2: Round-trip time interval, as measured on the earth
Will the round-trip time interval for the light pulse as measured on the earth be longer, shorter, or the same as the time interval measured on the light clock?
Will the round-trip time interval for the light pulse as measured on the earth be longer, shorter, or the same as the time interval measured on the light clock?
2. The round-trip time interval for the light pulse as measured on the earth be longer than the time interval measured on the light clock.
Question 3: Why does the moving light clock shrink?
You have probably noticed that the length of the moving light clock is smaller than the length of the stationary light clock. Could the round-trip time interval as measured on the earth be equal to the product of the Lorentz factor and the proper time interval if the moving light clock were the same size as the stationary light clock?
3. In order for the time intervals to obey this law, the length of the moving light clock had to be made smaller.
Question 4: The length contraction formula
A light clock is 1000 m long when measured at rest. How long would earth-bound observer's measure the clock to be if it had a Lorentz factor of 1.3 relative to the earth?
4. Lp = 1000m, γ =1.3. L=?
L= Lp/γ = 769m
proved!
Conclusion
This is a very useful lab and the website helps us to learn the special theory of relativity.
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