Particle in a Box

In the particle in a box active physics much was learned visually about the abstract world of modern physics. The two varying factors are the length and the mass. There are two wave functions that are simply psi and psi squared. Psi squared also actually equals the probability of the chance that particle is within a certain area.



The graphs also show a different value for the value of n which, the probability of finding the particle in that area is much higher as the values of n rise. As the length increases and decreases there are many changes that occur to these probabilities. The longest wavelength with a standing wave L is on that goes to twenty times ten to the negative fifteenth meters and the mass at the minimum must be 1.0 times the mass of a proton.

This is the energy of the ground state this can also be written as E = h^2/8mL this is the equation derived and given for an atom in ground state for a particle in a box. As the length of the box in this denoted as L increases then the value of the energy is decreased. It is inversely proportional to the ground state energy of an atom.


In this photo the value of the length of the standing waves has not been changed however the mass has been increased. Instead of being only the mass of one proton, the mass is now increased to five protons. This value makes the energy much lower. When the energy levels are higher the amount of energy is not nearly as high as any of the other energies as the mass is increased. Basically the higher the mass the lower the energy weirdly.

Active Physics Relativity

The active physics relativity gave a much more visual perspective of relativity. This included time dilation as well as length contraction. The field of simultaneity also applies which shows and proves that time is relative; depending on what frame of reference is given, each person has a different perspective on how fast something is traveling, the time it takes to reach that person and the contraction of the length given.



A time clock is given and it shows the time dilation when one is moving. If the value of gamma is higher, the time dilation is greater. This theory shows the effects of time travel that man has been forever struggling to do. This effect of time dilation has been proven in a way. Active physics is a great way to visually understand the effects of relativity.



The distance of the light travel is relative to how fast the movement of the frame is, however this only works at very high speeds and that any nonrelativistic speeds, this theory will not work. There are also many interesting things that happen at relativistic speeds such as the relativistic momentum and relativistic mass all depends on what frame on is in.


Relativity is basically just like a non relativistic depiction however whatever is the previous value of the time dilation and length contraction is just multiplied by gamma to find the change in time or length or even momentum. In the length contraction, the varying factor in the visual program is the length. When it shows that the length increases by a certain amount, then the time it takes for one light to get to the end increases giving the length a certain amount will be contracted.

Planck's Constant from an LED

In this experiment, the value of Planck's constant is to be measured using the wavelength of the different colors of the spectra. The theoretical value of Planck's constant is h = 6.626*10^-34 J s, but hopefully the actual value will be very close to that. There are several things that have been done in previous labs that will be used on this lab. The same setup as done with the color and spectra lab using 2 meter and 1 meter sticks to determine the wavelength of a given color. However, this time a different color light is given.


A diode is used in this laboratory which makes sure that the current does not flow in a seperate direction. There were four colors being tested and the voltage was given: red 1.87V, green 2.51V, Blue 2.62V, Yellow 1.89V. Using the equations Energy = charge of electron X voltage, and E= hc/lambda, E = -A/n^2, the wavelengths were calculated. Another measured distance was the distance from the light bulb to the color spectra. These were blue was twenty five centimeters, green 30 cm, red 37.5 cm, yellow 34 cm.


After many algebraic and geometric equations the values of planck's constant were fairly close to the calculated values. Values of 6.53 * 10^-34, 6.36 * 10^-34, and other values close to those values. However, like any other laboratory experiment there are possibilities of uncertainty. No matter how far one can measure something to, there will always be some value of uncertainty.



Human error in this lab is very high because it must be done with two people, making it harder to clarify what one sees. Of course, there is uncertainty in the other measurements as well such as the distance of the length from the LED to the diffraction grating.

Python Wave Function

This lab was a much different lab in all the rest because it required the use of computer programming using the language of phython. The ultimate goal or objective of this experiment is simply stated in the title. This allows students to be easier to visualize and see what is really going on to the uncertainty principle and how it relates to their construction. The programs that were used in this laboratory experiment was python, vpyton and pylab were to be installed prior to starting the lab.

Particles that are in a definite energy state like an electron bound which is not in an infinite energy level in an atom. The value of the absolute value of psi squared is independent of time, which is called a stationary state. If the definite energy E and the time dependent wave function can be written as a product of the time independent function and a function of time. The Schrodinger equation for a particle with definite energy E is:

Treating the wave function as a separable differential function, it can be seperated into a part that depends on x and one that depends on time. Taking the partial derivative with respect to time and the space portion constant comes out in front, this can be plugged back into the schrodinger equation and then divide both sides by psi of x times f of time. Rearrangement and cleaning up allows

The plot of a Gaussian distribution is one of the tasks for this assignment. In the informal form of psuedocode, the mean average and the standard deviation is set as constant, which is the followed by the coefficient of one over sigma root 2 pi. An initialized list called Gauss was then created and the function for gauss was coeff*e^-(x-avg)^2/2sigma^2. The final step was to write plot(x,Gauss). A graph that had a bell curve was then shown. This really shows that the probability that the particle is in a certain region gets much larger at a certain point and gets less and less at all other parts.

Another step or objective from this lab was to plot a sinusoidal function instead of a bell curve. This is surprisingly not that much more difficult, however it does require that some adjustments are made not only to the equation being used, but also to the boundaries of the sinusoid. The bounds used in this particular lab were set between the values of positive and negative pi. The program was also designed so that the amplitude and period of the sine function can be varied. This is accomplished by defining the variable of the amplitude. The frequency coefficient was also defined with a loop so that it could repeat itself to get a better view of whats going on.

The experiment was a different approach at tackling labs and understanding concepts because the probability of finding the particle and actually finding the particle cannot be determined using lab equipment found in community colleges. This laboratory may have been frustrating for some at first but once one gets the hang of it, it is not really that bad. Graphs of any type can be accomplished plotted and varied from any view. There is really no uncertainty in this lab which is one of the few labs like that. The only uncertainty is being uncertain that the program will work correctly.

Color and Spectra

Even though the experiment consisted of fairly simple materials, it produced interesting results.It was set up using a two meter stick a lamp and a one meter stick. The meter sticks were placed at 90 degree angles. They were stood up and used grating holders and the spectrum was measured. The glass or plastic slit that diffracts light used two slits of grating and it was placed at the end of the two meter stick.

Two triangles can be created using the wavelength, length of the distance of the diffractive glass to the light bulb and the distance calculated for each given color. When the eye moves outward from the center, light reaching it at a point along that color that was needed to be found gives the length d. For two similar triangles the ratio of equivalent sides of the two triangles are equal to one another.

As we measured each wavelength the purple was 393 nanometers, blue 446 nm, green 506 nm, yellow 507 nm, and red was 644 nm. There is a lot of uncertainty with these numbers because it is quite difficult to determine the exact location of the color spectra. This lab definitely requires at least two people to completely get done otherwise one cannot determine the location of distance from the light source to the designated color.



In the five thousand volt terminals of the power supply, the gas that was measured was mercury as the hidden gas. The lengths from the distance of the color from the light source was purple at 48 cm, green at 61 cm, yellow at 65 cm, red at 78 cm. Again these came to around values of 446, 515, 556, 588 nanometers which is in a fairly linear scale like it should be. There is a lot of uncertainty however because again human error makes a fairly large difference in the wavelength of the given color.

Experiment 10: Lenses

The objective of this experiment is to determine a relationship between the object distance d0, the image distance di, and the image height hi. This can be accomplished by increasing the focal length by an integer value each trial. The first step that must be done is to determine the focal length of the magnifying glass that is being used. This can be determined by taking the convex lense outside where the sun is and continue adjusting the length until the focal length can be determined. Measure this using a ruler and the focal length for the lense was 24.5 cm.

As the object distance is changed to half the focal length, the focal point could not be seen because the image was blurry and cannot be focused on. Graphs were to be plotted with the object distance vs the image distance with the object distance on the x values and the image distance on the y values.

This is not a linear graph but the graph of the inverse is more linear:

Using the computer's best line fit for the equation, the resulting line is y = -.87337x + .03788 which determines a lot about the graph of the inverses. The y intercept of .03788 determines the inverse of the focal length which is simply just 1/y intercept. The slope of the line indicates the relation of the focal point and the object distance. In the form of y = mx + b, the actual equation becomes 1/p = -m(1/q) + 1/f.


Just like any other experiment, there is always a certain amount of uncertainty. Especially with this lab and the lab where the width of a human hair is measured, slight uncertainty results can result in a much larger field of error. The most obvious uncertainty in this experiment comes from the human error. When the focal length was measured outside when using the sun as a source of light, many factors can contribute in giving an inaccurate measurement. However, the trial is done twice to minimize the amount of error given off by measurements. The other factor of uncertainty is basically the same thing, when one measures with the ruler, the measurements will always become off by a small but damaging amount.

Experiment 9: Concave and Convex Mirrors

This experiment contains very few materials since it is more of a conceptual lab. Most of the lab is done by just observations, and then applying those observations with the geometric drawing to determine whethere they agree with each other. The equipment or materials needed for this lab are simple: obviously a convex and concave mirror, a ruler, and an object. There are two main parts for each the convex and concave mirror. The first part consists of writing observations of how the mirrors play a role in the reflection of light waves, and secondly to determine the trigonometric angles to determine the height of the image and the magnification using scaling techniques.

The first part of the two mirrors is a convex mirror, which is a mirror that is rounded outward rather than inward. Any object will suffice such as my hand, and thus using this object in front of the convex mirror, the image appears larger in the middle, but smaller on the outside. The image on the mirror is upright rather than inverted. The image is located closer relative to the position of the mirror and object. As one moves the object closer to the mirror, the new image gets much larger fairly quickly. Likewise, as one moves the object further form the mirror than the previous observations, the new image gets much smaller quickly.

The second part of the convex mirror part is to determine the magnification of an image using simple geometric ways. The drawing above is basically recreated and the magnification is to be determined. The definition of magnification is the height of the image divided by the height of the object. The magnification of this convex mirror is .8cm / 3.3 cm which came out to be about .24x magnification. The observations did agree with the light ray sketch because the magnification is smaller.

For the concave mirrors, things are a little bit different than in the convex mirrors. Concave just means a mirror that is bent inward rather than outward which seems sort of like a cave hence the name. The image appears larger than the object instead of smaller like the convex because of the different ways the light reflects off the surface. The image also appears inverted from far, but upright from close. This must be because the focal point is in front of the mirror, rather than behind. So once the focal point is passed, the image becomes inverted. The image is located farther relative to the position of the mirror and object, whereas in convex it was the opposite.

After the observations of the concave mirror have been made, it is time to start the geometric applications of the light to this mirror. Just like how it was done for the convex mirror, a ruler will be used to show the reflection of the light rays bouncing off the surface of the mirror. The ruler is used to measure the distance of the object, the height of the object, the distance of the image, and the height of the image. In the end, the only two needed variables are the height of the image and the height of the object which are divided by each other to get a magnification of -.26x. This is nearly the same but negative as the magnification of the convex mirror. In a world without uncertainty, these would be exactly opposite values, but however due to human error and the thickness of the lead in a pencil, these will contribute factors of uncertainty. Even though they are minor and may be neglected, these are the only uncertainties that this lab will have.