Experiment 16: Measuring Planck's Constant

Purpose: 

Equipment:

• 
  

Experiment:

Conclusion:

Experiment 15: Color and Spectra

Purpose: To view the spectrum of colors found in white light and a hydrogen plasma tube in order to measure the wavelength of several different colors.
Equipment:

• Two meter sticks
• Metal clamps
• Flourescent lamp
• Hydrogen tube
• Diffraction grating

Experiment:

A diffraction grating was held infront of one of the student's eyes.

The student was then positioned ~1 meter stick away from the light source(flourescent lamp).

A rainbow appeared to the left of the viewer.

The distance of each color was then measured and recorded.
In addition to the spectrum of white light, a hydrogen plama light source was used.
This member created narrow distinct lines, as they appear in the picture bellow..



 The distances of the different wavelengths were then measured for this light source.

Data Analysis:
Using the geometric relationship of the wavelenght distance on the set right angle with the two meter sticks, the wavelengths were solved for

Conclusion:

The three different bands of light corresponding to violet, teal and red have acceptable values within their uncertainty.

All the calculated values for different wavelengths agreed within a 1% error of the theoretical values. 

Experiment 14: Potential Energy Diagrams & Potential Wells

Purpose: to use a computational model to analyze a potential energy diagram and well.

Part A) Potential Energy Diagrams

A particle of energy 12 x 10^-7 J moves in a region of space in which the potential energy is 10 x 10^-7 J between the points -5 cm and 0 cm, zero between the points 0 cm and +5 cm, and 20 x 10^-7 J everywhere else.

Question 1: Range of Motion
What will be the range of motion of the particle when subject to this potential energy function?

·         Range of motion is between -5 and 5 cm 

Question 2: Turning Points
Clearly state why the particle cannot travel more than 5 cm from the origin.

• the particle doesn’t have enough energy to surpass the potential barrier.

Question 3: Probability of Detection
Assume we measure the position of the particle at several random times. Is there a higher probability of detecting the particle between -5 cm and 0 cm or between 0 cm and +5 cm?

·         Probability of detection is higher between -5 and 0 because the particle spends more time there (less kinetic energy).

Question 4: Range of Motion
What will happen to the range of motion of the particle if its energy is doubled?

·         E=1/2kx^x, 2E>sqrt2x

Question 5: Kinetic Energy
Clearly describe the shape of the graph of the particle's kinetic energy vs. position.

• Kinetic energy vs potential is an upside down parabola with vertex at x=0

Question 6: Most Likely Location(s)
Assume we measure the position of the particle at several random times. Where will the particle most likely be detected?

• Most detected at extrema since kinetic energy is minimum

Part B) Potential Wells

A particle is trapped in a one-dimensional region of space by a potential energy function which is zero between positions zero and L, and equal to U₀ at all other positions. This is referred to as a potential well of depth U₀.

Examine a proton in a potential well of depth 50 MeV and width 10 x 10^-15 m.

Question 1: Infinite Well
If the potential well was infinitely deep, determine the ground state energy. Is this also the ground state energy in the finite well?

·         The ground state energy in an infinite well in greater than a finite well

Question 2: First Excited State
If the potential well was infinitely deep, determine the energy of the first excited state (n = 2). Is this also the energy of the first excited state in the finite well?

·         Energy of infinite=8.4 MeV. Not allowed in finite well.

Question 3: "Forbidden" Regions
Since the wavefunction can penetrate into the "forbidden" regions, will the energy of the first excited state in the finite well to be greater than or less than the energy of the first excited state in the infinite well? Why?

·         Energy infinite>energy finite; wavelength infinite<energy finite

Question 4: More Shallow Well
Will the energy of the n = 3 state increase or decrease if the depth of the potential well is decreased from 50 MeV to 25 MeV? Why?

·         If U decreases, then wavelength decreases

Question 5: Penetration Depth
What will happen to the penetration depth as the mass of the particle is increased?

·         If m increases, then penetration length decreases

Experiment 13: Relativity of Time and Distance

Purpose: to use computational models at near light speed scenarios to analyze relativity and time.

Part A) Relativity of Time

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?

The light in the moving car travels a longer distance than its stationary counterpart as displayed in the animation.

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?

The observable light in the moving car is relatively faster by a factor of 1.41 compared to the stationary counterpart.

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?

No, time appears to run at 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?

In decreasing the speed, the distance is decreased and the difference in time therefore decreases.

Question 5: The time dilation formula
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.

 

Question 6: The time dilation formula, one more time
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?

 

Part B) Relativity of Length

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?

Time does not 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?

The time interval will be longer as viewed on earth on the moving frame because there was a relative longer distance traveled by the light.

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?

No it is not equal because the length has decreased and the time has increased on earth(observer).

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?

Experiment 12: Optical Filters

Purpose: explore the effects of polorizing filters angled in respect to one another on light intensity transmitted.

Equipment:

• Polarizing filters
• Meter Stick
• Clamps
• Lamp
• Angle measured paper

Experiment:

Two Polarizing filter setup with light source shining through and lumens detector at end.

The angles were drawn in using an angle drawn circular paper



In the three polarizing filter experiment, we notice that with the first and last filters at 90 degrees with respect to one another, the middle filter must be at 45 degrees to maximize transmission of light.

Conclusion: 

Does the light from the fluorescent bulb have any polarization to it? If so, in what plane is the light polarized? How can you tell?

• No, the fluorescent bulb was not polarized as it did not have any shading on it. In addition, you can tell there was a single polarization filer cannot absorbe a significant amount of light, therefore two will be needed in order to filter enought of the transmitted light.

Does the reflected light have an polarization to it? If so, in what plane is the light polarized? How can you tell?

• Yes, the reflected light has polarization once the filters were set paralled to one another, turning pitch dark.

In addition, the only way to calculate uncertainty in this lab was the visualization of the cosine squared fuction on the logger pro.

The data plots were pretty sinosoidal and they appeared to support the conclusions in the questions asked.