experiment 13 meausre the wavelengh

Purpose:

the purpose of this experiment is to measure the wavelength of different light source.

equipment:

white light, unknown gas source, hydrgen gas source, ruler, diffraction glass.

Experiment and Data Collection:

first of all, we need to set up the equipment, we use two ruler, one is 2 meters, and another one is 1 meter long, fix them in right angle at the end of the two rulers. then put the light source in the corner of the two rulers, put a diffraction plastic card in oneside of the 2 meters ruler, then read the diffraction light through the diffraction plastic card in different color on the one meter ruler. the experiment has three part, first part light source is white light, second light source is unknow and we need to find the unknow of the light through the calculation, and the third is hydrgen light source.

we get the distance from the diffraction plastic card to the center of the white light L = 2.02 m

we get the slits of the plastic card is d = 1.76*10^-6 m

for all the three part of the experiment, the two data above are the same.

then we use equation formula λ= d*D/(d^2+D^2)^1/2, to calculate the wavelength of the light source in different color.

First part white light source:

Color	Distance /m	Wavelength /m
Violet	0.478	4.05*10^-7
Blue	0.569	4.77*10^-7
Green	0.63	5.24*10^-7
Yellow	0.64	5.32*10^-7
Orange	0.679	5.61*10^-7
Red	0.804	6.51*10^-7

Second part unknow light source:

Color	Distance /m	Wavelength /m
Violet	0.474	4.02*10^-7
Green	0.593	4.96*10^-7
Yellow	0.64	5.32*10^-7
Orange	0.67	5.54*10^-7
Red	0.79	6.41*10^-7

after we compare the wavelenght to the spectru table, we consider our unknow is mercury.

then we need to find the calibration equation of our equipment to reduce the error for our third part experiment, we get the actual wavelengh of the mercury for three color, then make a graph that actual wavelengh vs the experiment value of the wavelengh.

Color	Y /nm	X /nm
Violet	430	402
Green	548	496
Yellow	577	532

from the graph we get the calibration equation is y = 1.1559x - 32.641.

Third Part:

the third part we need to measure the hydrgen gas light wavelength, then we need to calibrate.

Color	D /m	Wavelength /m	After calibrate /m	Wavelength actual/m
Violet	0.48	4.06*10^-7	4.37*10^-7	4.34*10^-7
blue	0.588	4.92*10^-7	5.36*10^-7	4.86*10^-7
red	0.742	6.07*10^-7	6.69*10^-7	6.56*10^-7

after the calibration, we compare he wavelength to the actual wavelength, the Violent, and red color compare to the actual value are very close, but the second blue color compare to the actual wavelength, there are about 50 nm off.

Conclusion:

from thsi experiment ,we are successful find the wavelength of different light source in different color, but still have some error percent.

Experiment 12

Purpose: the purpose of this lab is to learn qantum mechanics the particle in a box

1. the longest wavelengh is 2L

2. the longest wavelengh is h/2L

3. En = pn^2/2m = n^2pai^2h^2/2mL^2, when n = 1, is ground energy

4. if the L increasing, the ground energy will decrease.

5. as the size of the box is increased, the ground state energy decreass and the allowed energy levels become closer together. if you could increase the size of the box to a macroscopic size, the ground state energy would be etremely close to zero and the allowed energies would be extremely close to zero and the allowed energies ould be extremely close to continuous. thus, in a macroscopic box, you can be at rest and have any value for your energy.

6. L is very large, energy decrease.

7. ground state

8. it does not depend on the mass of the particle, depend on the size of the box.

9. yes, true.

10. yes.

experiment 11: python

from pylab import*
cener = 5
sigma = 1
coeff = 1/sqrt(2*pi)*sigma
gauss_list = []

for x in arange(0,10,0.1):
gauss = coeff*exp(-(x-center)**2/(2. *sigma **2))
gauss_list.append(gauss)
plot(gauss_list)
show()



from pylab import*
center = 0
sigma = 1
gauss_list=[]
k = 1
z=[]

for x in arange(-pi,pi,pi/128):
gauss = sin(k*x)
gaus_list.append(gauss)
z.append(x)
plot(z,gauss_list)
show()





from pylab import *
A= 1
w = 1
Fourier_seriers = []
for i in range(1,3):
x = []
sine_function = []
for t in arange(-3.14,3.14,0.01)
sine_function.append(sine_function)
x.append(t)
Fourier_Seriesappend(sine_fucntion)

superposition = zeros(len(sine_function))
for function in Fourier_Series:
for i in range(len(fucntion)):
fuperposition[i]
plot(x,superpositon)





from pylab import* #Need this for plotting functions
Number=50center = 0 #Define the center of the gaussian constants
sigma = 1 #set the standard deviation to 1
coeff = 1 / sqrt(2*pi)*sigma #This is the normalization
coefficientstgauss_list = [] #Create a rom list of the values in the Gaussian
#Calculation loop
for x in arange(0,Number,0.1): #Loop from 0 to 10 by 0.1
gauss = coeff * exp (-(x-center)**2/(2. * sigma **2)) #Find the Gaussian gauss_list.append(gauss) #Add the calcualted values to the list of values#plot(gauss_list) #Plot the values
#Define the Amplitude of the Sine Functionw = 1 #Set the frequency coefficientFourier_Series = [] #Iniialize the list of sine functions#Calculate the harmonics of the sine functions
for i in range(1,Number): x = [] #This will let us plot the values from -pi to pi sine_function = [] #This contains the sine function for t in arange (-3.14,3.14,0.01): #loop from 0 to 10 by 0.1 sine_f = gauss_list[i-1] * sin(i*w*t) #Calculate the sine sine_function.append(sine_f) x.append(t) #plot(x,sine_function) #Plot the values Fourier_Series.append(sine_function)
superposition = zeros(len(sine_function)) #set as zeros of length equal to the sine
for function in Fourier_Series: for i in range(len(function)): superposition[i] += function[i]
plot (x,superposition)
show () #Show the plots

experiment 10 Modern Physics: Relativity of Time

1.Question: Distance traveled by the light pulse
anwser: 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 is larger.


2.Question: Time interval required for light pulse travel, as measured on the earth
anwer: the time interval of the moving top mirror is larger.

3.Question time interval required for light pulse travel, as measured on the light clock
anwer: when I riding on the light clock, in my frame of reference, the light pulse travel a larger distance to completer a single round trip.

4. Question the effect of velocit on time dilation
anwer: the difference in light pulse travel time between the earth's timers and the light clock's timers decrease as the velocity of the light clock is decreased. 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 thsi distance difference decreases, the time difference also decrease.

5. Queston: the time dilation formula
anwer: the proper time interval, the time interval measured by an observer riding the light clock, is 6.67us, the proper time interval does not depend on the speed of the light clock. the time interval measured by an earth-bound observer is the product of the proper time interval and the lorentz factor. thus, the time interval measured by an earth bound observer is 1.2 * 6.67us = 8us.

6. Question: the time dilation formula, one more time
answer: the proper time interval, the time interval measured by an observor riding the light clock, is 6.67us. the proper time interval does not depend on the speed of the light clock. the time interval measured by an earthbound observor is 7.45 us. the lorentz factor is the ratio of the earth-bound observor's time interval measurement to the proper time interval. or 7.45/6.67 = 1.12

Experiment 9 CD diffraction

Purpose:

The purpose of this experiment is to find the groove on the CD use the diffraction method

Equipment:

CD, laser pointer, CD holder structure, board, laser pointer holder, ruler.

Experiment and Data Collection:

We set up the structure like the picture does. Let the laser beam point to the surface of the CD, and use the white board receive the diffraction pattern from the CD.

From this experiment we get data:

The left first maxima distance = 12.9 cm

The right first maxima distance = 13.1 cm

And we use get the distance from the CD to white board L = 17.0 cm

We have the wavelength of laser wavelength from professor is about 670 nm

The equation we use is d = m*wavelength/sinθ, first maximum m = 1, for the angle is very small, so θ = tan^-1(x/L), use this equation we can find the angle θ, furthemore we can get sinθ. Then us equation d = m*wavelength/sinθ, we already know sinθ, m and the wavelength of the laser beam, we can find d.

We get two d one is for the left first maximum: d = 1.1 * 10^-6 m.

We get another one is for the right first maximum: d = 1.08 *10^-6 m.

we get the fact value of the distance between the CD grooves is: 1600nm.

But our experiment value range is smaller compare to the real value.

Conclusion:

in this experiment we learn how to use the diffraction method to find the distance between the CD grooves, and we finally find the distance, but our value is smaller compare to the expect value. We think there are some reason make these error percent, so our experiment is off a little bit. First reason is our measurement with the ruler have some error percent, we may record the value are not accurate, second is the laser pointer position is not vertical to the surface of the CD surface.. Third reason is our set up structure is not stable, may have some change during the measurement cause the error percent.