Experiment 16: Determining Planks Constant

PURPOSE: In this experiment a circuit will be assembled to measure the voltage across an LED and wavelength will also be calculated which will lead to the calculation of finding h, Planks Constant, which has a value of 6.626 X 10^-34.

PROCEDURE:

red LED across voltage in series

View through slit

View through slit of white light.

 DATA & ANALYSIS:

Measurement of Voltage and Distance (D) of spectra
LED	Red		Blue		Green		Yellow
Voltage (V)	1.884 ± .01		2.711 ± .01		2.825 ± .01		1.924 ± .01
Trial 1 (cm)	67.25	61.2	69.2	44.75	66.0	50.0	65.5	55.5
Trial 2 (cm)	69.9	61	57.5	44.75	64.0	51.8	65.0	54.5
Trial 3 (cm)	68.0	60.0	57.8	46.0	63.0	50.25	63.8	54.5

CONCLUSION: There were many steps taken to find and verify planks constant. Using a number of different LED lights, the wavelength was determined by finding the distance of the spectra and using the law of similar triangles. The voltage was also determined which would be used along with the known charge of an electron to find the energy, E of the system. Using the value of E and the calculated wavelength of each light, planks constant was able to be determined. The slope of E and c/λ, the value would give the value of the planks constant from the values of LED lights. However, the given value as shown gives a high error value.
Planks constant is known to be 6.626E-34, and the slope value had given a value on the order of 10^-33. Because of this error, the experiment then relied on the theoretical approach of calculating the h value of each LED and finding the average value. This had given a value of 10^-34 and more specifically an error with 15% which is an accepted value. Based on these values planks constant is verified based on these results.

Experiment 15: Quantum Mechanics: Potential Energy Diagrams

PURPOSE: To observe and understand potential energy in Quantum Mechanics and verifying the probability of finding particles. 

1. The range of motion is between -5 and 5 cm.

2. The particle does not have enough kinetic energy to pass through that boundary. 

3. There is a higher probability of finding the particle from 05 to 0 cm because it has a higher potential energy on that side. 

4. The range of motion increases when the energy is doubled. 

5. The graph is an inverted parabola.

6. The particles will be most likely found at the ends where the boundaries are located.

1. 

E = n² h² / 8 m L². 

E = (1)² (6.626 x 10^-34 J s)² / 8 (1.673 x 10^-27 kg) (10 x 10^-15 m)²

E = 3.3 x 10^-13 J 

E = 2.1 MeV 

2. 4(2.1eV) = 8.4 MeV for infinite well but not for finite well

3. In the infinite well it is has larger energy in its first excited state because it has a shorter wavelength than in the finite well

When the potential energy is decreased, the total energy of the n = 3 state decreases as well because the U(x) function decreases the area the particle can be in and the wavelength decreases.

The penetration depth decreases as the mass increases. This is because the mass is becoming measurable and cannot travel in to the forbidden region. 

Experiment 14: Color and Spectra

PURPOSE: In this experiment, the spectrum of colors were viewed in white light and the light from colored filters that contains hydrogen gas.

FORMULAS & DERIVATIONS:

Illustration of the experiment. An observer will see through the double slit which has a grating of about 500 lines per mm. 

Using similar triangle technique, the following derivations can take place.

PROCEDURE:

SETUP OF EXPERIMENT

Top View

The distance of the color spectrum was measured from the light source.

The color spectrum of white light

Spectra of a Hydrogen gas

Setup with Hydrogen Gas as the "light source"

Spectra of Hydrogen gas. 

DATA & ANALYSIS

Measurement of the white light spectra:

Calculation to determine wavelength for both ends of the spectrum. Note d is given by the double slit (there are 500 lines per mm). The slit was 1.89 meters away (L). The distance of the light, D was a measured value with uncertainty.

Uncertainty was measured through standard deviation. The Theoretical values for the visible spectrum was given and the uncertainty lies within the true values of the wavelength.

Calibration of the wavelength was determined on the right side of the board using both the experimental and theoretical values of the wavelength.

Measurement of Hydrogen Gas

Calculations for the different colors presented in the spectrum. The yellowish-green color was not calculated since it is not in the spectrum of hydrogen gas, and perhaps it was light interfered from another source. 

Calculation of the theoretical wavelengths of  hydrogen gas using the Bohr Model. 

ERROR ANALYSIS

The uncertainty does not lie within the actual values based on the standard deviation model of uncertainty, and the wavelength between the 1st and 3rd line was not visible to the naked eye

CONCLUSION:

The spectra of visible light from the white light was verified and based on the uncertainty the values were also verified by the theoretical values. The white light helped find a means of calibration for the next portion of the experiment in order to verify the spectra of hydrogen. There were only three of the four lines that were seen that would indicate hydrogen in the spectra. The reason for the λ₂₄   to not be seen is that it was too close to the other lines which made it harder to see with the naked eye. The values of the wavelengths from the experimental side however could not verify the the theoretical values of hydrogen based on the uncertainty which was determined by standard deviation. Consistently, the experimental wavelengths all fell shortly under the true values of the wavelength. When calculating percent error the values all fall under 8% error which shows both precision and accuracy in the experiment. Therefore, the spectra of hydrogen can be verified in this experiment. Although, the second line could not be seen, based on the theoretical calculations there seems to be a hole where the value should be indicating that this spectra does indeed belong to hydrogen. 

Experiment 13: Relativity

PURPOSE:

Relativity in Time:

Distance was calculated by the light traveled in a stationary frame and the distance traveled in a moving frame.

Time was claculated that it takes for the moving frame compared to the rest frame. when the moving frame is recorded by a stationary observer it takes longer. This is because the light needs to travel a larger distance but only at the speed of light. 

Time was measured both by a stationary observer and an observer in the moving frame. the observer in the moving frame obtains the same time as a stationary observer in the stationary frame. This occurs because relative to the observer the light only has to travel up and down. The time measure by a stationary observer is longer regarding the moving frame. 

As the velocity approaches a smaller number, the gamma also gets smaller.  

The proper time is equal to 6.67 microseconds. Using a gamma of 1.2 in the equation t'=gamma*t, the resulted time is equal to 8.004 microseconds.

PROPER LENGTH: 

The time does not depend on whether the light is moving stationary relative to the earth. 

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. 

The Round trip time interval thats measured on the earth would not be equal to the product of the Lorentz factor, and the proper time interval of the moving light clock. They are not equal because the length has decreased and the time has increased on the earth.

A light clock is 1000 m long when measured at rest. If the lorentz factor is 1.3, then the length of the earth bound clock would be about 769m.

Experiment 12: Polarization

PURPOSE:

The purpose of this experiment was to observe the change in light intensity through polarizing filters and measure the transmission of light as a function of the angle between the axes.

PROCEDURE:

Polarization angle was set to 0 degrees by setting the two vertical to each other;
The light source measured the "least" amount of light when it was 0 degrees.

Angle and the light intensity was measured using the setup of the apparatus 

As the two polarizers were rotated at different angles, the intensity of the light had changed. Completely parallel showed the highest amount of light intensity, while the lowest showed perpendicular. 

Third polarizer was added perpendicular to the first polarizer. The second polarizer (middle) was adjusted to measure the angle for each measured intensity. 

Light intensity was measured by logger pro. 

DATA & ANALYSIS

Two Polarizers:

Three Polarizers:

CONCLUSION

As the the first polarizer is set to 0 degrees, the the second polarizers is perpendicular to the first and third one letting only the minimum amount of a light. When the second polarizer is moved to the 45 degree position the amount of light from the first polarizer is half and from the second to the third is half, giving its maximum value. Based on the given data, it can be concluded that the light intensity does depend on the angle of the polarization and depending on whether the polarizition is parallel or perpendicular, the amount of light is at its maximum or minimum.