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## Alpha Particle Spectroscopy

FIG.1

FIG.2

The Alpha particle contains two protons and two neutrons identical to the structure of Helium-4 nuclei (so alpha particle has a +2 overall charge), which is generally produced in the process of Alpha decay. Alpha particles are commonly emitted by all of the larger radioactive nuclei. The atomic number goes down by exactly 2, as the result of losing two protons.They are highly ionizing form of particle radiation, and have low penetration depth. Thus, they are easily stopped by a few centimeters of air.

The purpose of this lab is to investigate the interaction of alpha particles and air molecules at different atmospheric pressures by observing the alpha spectra emitted by Americium-241( the source of our experiment). The alpha particles are detected by a silicon surface barrier detector placed in a vacuum chamber. A vacuum gauge will monitor the pressure inside the chamber.

Two major elements will affect the gain (resolution of the spectrum) of the detector. First is the pressure in the chamber and the other is the voltage applied to the detector. The setup of the experiment is indicated as in Figure 1 and 2 and most of equipment are labeled. The Am-241 source is placed in a stainless steel vacuum chamber, a pump is used to evacuate the air inside the chamber because the alpha particles has very low penetration depth. The pressure inside of the chamber has to be around 0 Torr in order to get a high resolution spectrum. In this case, we fix the atmospheric pressure to 0 Torr, and applied different voltage to the detector. An Ortec 428 detector bias supply is used to apply voltages for the Detector. Data was taken at three different voltages: 25V, 60V, 95V and 125V. Based on the data, the spectrum is cleanest at 125V. In other word, under 125 voltage, the spectrum has the most distinguishable peaks and the FWHM is the smallest. So the voltage for taking data acquisition is fixed to 125V from now on.

The major experiment consists two part. First, we want to correlate the channel number in MCA with energy using the 10-hour-data acquisition for Am-241 and its characteristic peaks: 5.38 MeV, 5.44 MeV, and 5.48 MeV with their corresponding channel numbers. Second is to investigate the energy loss when increase the pressure inside the chamber.

Following diagram shows the three characteristic peaks for Am-241 for 10 hours data acquisition of alpha spectrum:

Using Gaussian distribution we can do the fitting. We are able to approximate pretty accurate mean for each peaks which indicate the channel number corresponding to each characteristic peaks. For 5.38 MeV, 5.44 MeV, and 5.48 MeV peaks, they have corresponding channel number 7377(2), 7451(2), and 7495(2). A linear line for correlating the channel number and the energy can be plotted:

The equation of the linear fit is:

Channel Number =1184.2*Energy (MeV)+1006.8.

Since the Energy is already correlated with Channel Number, we can investigate the energy of alpha particle detected at different atmospheric pressures. The alpha spectra of Am-241 taken at different levels of vacuum are shown in the following figure (each peak is collected with 5 minutes data acquisition) :

The pressure is increased at a step around 30 Torr. The peaks along the x-axis corresponds to the pressure ranging between 420 to 33 Torr. We can plot a graph to show the relationship between the peak energy versus the pressure to study the interaction between the alpha particle and the air molecules:

As we can see from the figure above, the higher the pressure in the chamber gets the lower the peak energy is. So, only the alpha with very low energies made it to the detector.

Also, we can investigate the energy of alpha radiation detected under different thickness of air. The absorber thickness is defined as the distance between the detector (5.9 cm) and the source multiplied by the ratio of chamber pressure to the air pressure(720 Torr):

The following figure shows the absorber thickness versus the energy detected alpha radiation:

Form the figure above, we see the expected trend: as the the absorber thickness increases, the energy of alpha particle detected decreases.

The stopping power curve (dE/dX versus absorber thickness) thus can be plotted using the adjacent figure above. The difference between each x value is dx, and the difference between each correspond E is dE. Thus, the dE/dX can be calculated. The stopping power curve is displayed following:

The result is consistent with the previous report value of dE/dX which is around 2.

Summary:

I should take more data at higher pressure next time to get a more complete power stopping curve.

## Millikan Oil Drop

FIG.1: Set up of the experiment

FIG.2: A spacer between a two-plate capacitance.

The electric charge carried by a particle may be calculated buy measuring the force experienced by the particle in an electric field of known strength. The purpose of this lab is to calculate the electric charge carried by a oil drop, and determine how many electrons are on the drop. I determined that approximately 296 electrons are carried by an oil drop with terminal velocity 4x10^-4m/s. This is done by measuring the force experienced by the particle in an known electric field. In this experiment, the behavior of a oil drop with masses of 10^{-12} g or less is studied, and is observed in a gravitational and electric field. The second part of the experiment includes measuring the velocity of the oil drop if let it get exposed under the ionization source. Analyze the velocity change of the oil drop to calculate how much electric charge can be changed during the exposure period.

The analysis of the forces acting on an oil drop will yield the equation for the determination of the charge carried by the droplet. A oil drop in a electric field will experiences three kinds of forces. One is the electric force, one is the gravitational force and the other one is friction. Due to the experiment set up, the direction of gravitational force is always opposite to the direction electric force, and the direction of the friction is opposite to the direction of the movement of the oil drop. If we set v_o is the terminal velocity of fall, k is the coefficient of friction between the air and the drop (which can be represented as -mg/v_o, m is the mass of the drop, g is the acceleration of the gravity, E is the electric field, q is the charge carried by the drop, and v is the velocity. We have following equations:

(1)

where E is the voltage applied divided by the distance between the two plates (which is the thickness of the spacer between two places as indicated in Figure 2). lets denote s as the slope of the plot of v versus E:

(2)

so q which is the total charge carried by a oil drop equals to:

(3)

where m can be expressed for the volume of a sphere as:

(4)

where a is the radius of the oil drop, one can expressed a using Stokes’ Law, relating the radius of a spherical body to its velocity of fall in a viscous medium (with the coefficient of viscosity, eta):

(5)

where p is the barometric pressure which equals to 101.3x10^3 Pa, eta is the viscosity of dry air which has a linear relationship with the temperature, and b is the constant, which equals to 8.22x10^-3 Pa*m.

Using equation 3 and equation 5, the total charge carried by a oil drop can be writen as:

(6)

where the density of the oil is 886kg/m^3. We are able to determine the the viscosity under experimental condition later according to the linear relationship between the temperature and the viscosity of the air.

Proceed to the experiment setup as indicated in Figure 1 and 2. The apparatus consists a DC voltage supply to create the electric field wanted. A capacitance that has a plastic spacer between them, the thickness of the spacer is measured to be 1cm. Here are two plates of this capacitance, one positive and the other negative. The capacitance is placed within a chamber and the upper plate has a small hole in the middle where we can introduce the oil drops using a atomizer. Through a short vocal distance microscope, the oil drops can be viewed. The viewing scope has grids, whose major lines were separated by 0.5 mm, that simplify the measurement of the fall and rise distance of a oil drop.

According to equation 6 introduced above, total charge carried by a single oil drop can be calculated if we know the terminal velocity of the drop. In order to get the terminal velocity of a specific oil drop, I measure the time for a same oil drop rise and fall (caused by changing direction of the field) under varies electric field generated by 100V, 200V, 300V, 400V and 500V, so the velocity of the oil drop in different field can be approximated. We analyzed above , depending on the type of charge carried by this oil drop, the electric force would speed up the rise and fall speed of the drop and the gravitational force would speed up the falling velocity. If we plot the graph for the velocity of oil drop versus the strength of the electric field, we should expect as the strength of the electric field increases, the average speed of the oil drop increases as well.

Following we show the graph for the fall and rise velocity of the same oil drop under different electric field. I use a linear fit to do the curve fitting.

FIG.3

Theoretically, we can read the V_0 from the graph, V_0 is approximated to be 4x10^-4m/s. According to equation 6, we can calculate the total charge carried by this oil drop once we get the value of V_0 and S (S is the slope of the linear fit times the distance between the two plates according to equation 1). The total charge carried by this oil is 4.74x10^-17 C and it approximately carries 296 electrons.

The second part of the experiment evolves measuring the velocity of a oil drop if let it get exposed near a ionization source. The ionizaion source will add excess electric charge on the droplet after the exposure and it will change the terminal velocity of the oil drop. By measuring the velocity of the drop, the amount of increasing electric charge can be calculated. we pick one oil drop and record the time it takes to drive up and down for several times without turn on the ionization source. Then, we hit the ionization switch for a few seconds and repeat the process. Following chart shows the velocity of the same oil drop before and after get exposed to the ionization source.

The equation for calculating the electric charge carried by the oil drop is:

(7)

where v_f is the falling velocity, v_r is the rise velocity, and the other parameters have the same definitions as defined before. Using equation 7, I calculate the electric charges carried by the drop both before and after exposed to ionization source, and divided them with the electric charge of the the electron and round up the result. Initially, the droplet has 306 electrons. After 5 second exposure, the number of electrons carried by the droplet increases to 677. After 8 second exposure, due to the fact that the electrons on the the droplet was stolen by another droplet, the number of electrons carried by the droplet decreases to 62.

## High Resolution Gamma Spectroscopy

In this experiment, using high purity Germanium semiconductor detector with the MCA, a total six gamma spectra were measured. Mechanisms of gamma spectrum were explained as well. From the energy of gamma rays emitted by radioisotopes, a calibration curve was plotted to correlate the linear relationship between gamma-ray energy and MCA channel number. The best fit line matched the data with a least squares fit R^2=1. The purpose of the experiment is to determine the possible radioisotopes inside the sample sources-Brazil nuts utilizing the gamma spectroscopy. Using the correlated energy, the photon peaks existed in the Brazil nuts gamma spectrum can be read out. By Matching the gamma energies of these photo peaks to the known energies emitted by certain radioisotopes, the possible radioisotopes inside of the Brazil Nuts were determined. At least two major gamma radiations (with the highest and the second highest intensities) of the same radioisotope can be identified from the gamma spectrum of Brazil Nuts. We found there are three possible radioisotopes inside of Brazil Nuts: Ra-224, K-43, and Pa-234.

A high resolution liquid nitrogen cooled Germanium crystal detector is used in this experiment. We keep the temperature of liquid nitrogen fixed at 77k. Gamma’s are emitted when unstable quanta decay to other nuclei, sometimes by emitting electrons or positions. The energy of Gamma radiation can be very high (range from kev to several Mev). In the experiment, the high energy gamma emissions are absorbed by the cooled Germanium crystal. When gamma enters the detector, it scatters an electron, and liberates the localized electron from the valence band into the conduction band. A lot of kinetic energy are giving out through the process. The first electron can then collide with other electrons giving up it kinetic energy to the excitation of other electrons from the valence band to the conducting band. Meanwhile the scattered gamma may escape or it may collide with another electron, losing more of its energy to the excitation of electrons into the conducting band. A high voltage is applied to sweep the electrons from crystal before they lose energy and fall back into the valence band. (we use liquid nitrogen to cool the detector because the high voltage might thermally excite the electrons in the conducting band, so it will cover up the signal produced by the gamma emissions). The liberated electrons are accumulated on a capacitor in a preamplifier, where the charge on the capacitor results in a voltage proportional to the amount of charge. This voltage is thus also proportional to the gamma ray energy. When the capacitor is discharged, current produced by electrons forms signal pulses. Through preamplifier, the signals are increased. Then, the signals are sent to the Amplifier internal to the muti-channel Analyzer (MCA), where the pulse size can be intensified again and shaped into a 1 us long and 0-5v high pulse. The MCA measures the height, digitizes it and converts the height into numerical values form 1-8k, and counts the number of the pulses with each integer value of pulse height . Finally MCA creates a histogram to show the number of pulses with that height versus the channel number. The height of pulses (proportional to the gamma energy) is plotted on the horizontal axis of the display and are referred to as channel number. The setup of the experiment is shown in the following figure:

A total six gamma decay spectra of the radioactive sources are measured. Four of these sources are used for calibration of the energy and MCA channel number: Cobalt-60, Cesium-137, Sodium-22, and Barium-133. Two of there sources for determine the radioisotopes inside Brazil Nuts: Background and Brazil nuts. From 12 of gamma-ray energies with their corresponding channel numbers, a calibration curve can be plotted. The best fit line with the calibration curve proves that the MCA channel number is proportional to the energy of the original incident gamma. Using the cribration curve, the energy of photo peaks in the Brazil nuts spectrum can be determined. Thus, the possible radioisotopes inside Brazil nut can be identified.

Before taking the measurement, there some background we should know about the gamma particle interaction. Since the gamma-ray photons do not have an intrinsic charge, photons themselves are invisible to the detector. The measurement of these photons depends on their interaction with the electrons inside the detector (in this experiment, a pure single crystal of the semiconductor material germanium is used as the detector). The incident photons interact with the electrons which we look at to understand the nature of the photon itself. Gamma ray energy is deposited in the detector and the detection system measures the energy given to the electrons. There are three ways a gamma-ray can interact with its medium: photoelectric absorption, Compton scattering and pair production.

The spectrum of Cobalt-60, Cesium-137, Sodium-22, and Barium-133 are shown below. The corresponding channel number of photon peaks can be read out from the spectra.

Cesium-60:

Sodium-22:

Barium-137:

Cobalt-60:

So the channel number can be correlated with the Energy:

So using the calibration line, the photon peak shown in the gamma spectrum of the Brazil nut can be identified. The gamma spectrum of the Brazil nut is shown in the following:

From the gamma spectrum, the corresponding energies of the six peaks can be read from the gamma spectrum. By searching the energy of gamma rays emitted by radioisotopes, we are able to match the six peaks to the gamma rays emitted by three radioactive isotopes: Ra-224, K-43, and Pa-234.

## Fourier Optics

In this lab, experimentally, we reproof that electromagnetic waves passing through an aperture should form a Fourier transform of the aperture. It shows the practical application of Fourier transformation.

For the set up, we are using an optical system(Shown following):

The setup of the experiment contains a Neon-Helium laser, three plans, three lenses, and a digital camera connected to a computer with the uEye program. The laser that we used has a “spatial filter”(which denoted as SF) on front. A spatial filter is a kind of optical processor that eliminates high frequency noise on the leaser beam. So, a uniform diverging beam can be seen coming out of the laser. Plane P1 is where the original object is placed. Lens L2 then takes a Fourier transform of the object, which appears in Plane P2, Fourier plane(where the slit is placed for the Fourier transform to occur). Next, L2 takes an inverse Fourier transform to recreate an image of the original object, which appeared on Plane P3. Finally the image is captured by the camera.

Begin with the simple pattern(object): the Fourier transform of a grid. The two dimensional Fourier Transform is:

Two images are being shot. One is on P2, the other one is on P3.

Following is the image being shot on P3, which is the unfiltered the image of the grid:

Than is the Fourier image of unfiltered image.

Using a 0.16 mm diffraction slit, I am be able to block out all horizontal component of grid. Following image, horizontal lines of grid, is the final image captured by the camera.

Changing the orientation of the diffraction of the slit. I am able to block out all vertical component of grid. Following image, vertical lines of grid, is the final image captured by camera.

We can conclude that the Fourier Transform of a grid is a superposition of Fourier transforms of a vertical and a horizontal slit. The edges of the slit are determined by the highest frequencies. We can find corresponding relationships in mathematics. The Fourier transform of the edges of a sharp function are determined by highest frequencies too.

Next, I try a low contrast object, a fingerprint on a glass slide. In order to enhance the contrast, I put a constant block at the middle Fourier transform, using a diffraction slit with a small dot in the center. We know that the Fourier transform is the sum of all frequencies. To make the function with sharp edges(rectangular), the series has to go to very high frequencies. So we need to block the low frequency part, which is in the center, to enhance the contrast.

Following is the image of Fourier transform of the fingerprint.

Next image shows the filtered image of finger print after using the dot diffraction slit. (To enhance the contrast)

From the graph, though my enhancement is not successful, however, we can tell the image of a finger print.

For the final part of the experiment, I use a glass slide said: “text” with vertical lines running through it.

Following is the Fourier image of the image:

We want to block the vertical lines, using a vertical slit.

Following is the graph of the filtered Fourier transform of the image.

In this lab, we explore the use of lenses and its corresponding relationship with Fourier Transform. We also explore how filters can be used to manipulate images.

## e/k Ration&Transistor Band Gap

In the e/k ratio and transistor band gap experiment, I investigated on the current-voltage relationship of a p-n junction(I used silicon as my transistor) is measured at different temperatures, permitting a determination of the ratio of e(the magnitude of the charge of an electron to k(Boltzmann’s constant). The experiment is based upon the fact that the short-circuit collector current in silicon transistors operated in the common base mode is an exponential function of the emitter vase voltage over a wide range of currents. Therefore, a graph of current vs voltage on a semi log graph paper can be showed in a straight line with slope of e/KT. Through the experiment, I will record temperatures, changing current voltage and correspond current in each experiment.

Following equation shows the e-k relationship:

The circuit used in the experiment is presented following:

The measurement is recorded under five different temperature conditions-room temperature (299k), at water/ice mix temperature (277k), at boiling water (370.7k), dryice in the isopropyl alcohol (197.2k), and liquid nitrogen (79k). First three measurements are preceded in the test tube filled in with oil. Put a mercury thermometer in the oil with the semiconductor (note that all measurements should use the same semiconductor), a quick measurement for I and V can be made. I recorded our the data for I and V with uncertainties and a figure showing the linear relationship between ln(I) and V can be plotted. Results for my plotting are showed below:

Form the figure we can see that as the temperature decreases and the initial voltage increases, the slope of the line increases. The result is under our expectation, since the ek/T is inversely related to the T.

Finally we can using the data obtained above to plot ek/T against 1/k as shown below to get the slope which indicates value of e/k (which is approximately 8935.1 V/T), and multiple the value of k we can get the energy gap. From the experiment the estimated energy gap is 1.23 eV which consistent with the accepted range(1.11-1.13 eV).

From NIST, we can find that k = 1.380 x 10^{-23} J/K.

## Optical Spectroscopy

There are two common ways of separating light by its wavelength so that such spectra can be measured. One uses a prism, in which the dependence of the index of refraction of the glass on wavelength means that there are different angles at which the light rays are bent. After passing through two sides of the prism, the incident light is separated into its colors, each of which travels in a different direction. The second way uses a grating, light scattered from each of the rulings on the grating will interfere in specific directions depending on the angle of incidence of the light and spacing of the rulings on the grating. In the experiment I will use the diffraction grating to acquire dispersed emission spectra of the light output of several lamps(Mercury, Hydrogen, and Deuterium lamps).

The purpose of the experiment is to determine the mass ratio of Hydrogen and Deuterium via analysis of Hydrogen/Deuterium optical spectral lines. This paper shows how to measure the spectra of Hydrogen and Deuterium emissions using a grating spectrometer and a gas discharged lamp contains Hydrogen enriched with Deuterium, from the measured isotope shift in four Balmar transitions to determine Deuteron-Proton mass ratio. For H_alpha transition, mass ratio of m_D/m_p=2.08 with uncertainty 0.07, which agrees with the accepted value 1.99900750097. However, for higher transition orders (beta, gamma, and delta), due to the weak intensity of emission lines and small wavelength shifts, it becomes harder to identify two peaks, and the mass ratios obtained deviate from the accepted value. The four measurements give the weighted mass ratio m_D/m_p=2.39 with uncertainty 0.05. An discussion is carried out to analyze the experiment result. Following is the diagram shows the set up of the experiment:

To obtain high-resolution spectra of the Balmer lines of atomic Hydrogen and Deuterium, we use a Deuterium lamp and a grating spectrometer controlled by the LabView program running on the computer as indicated in the figure above. The setup includes a monochromator (HR-320), a PMT and a Deuterium lamp. HR-320 (which can be used as a spectrograph or as a scanning monochromator) produced by I.S. instrumental company is used as the scanning monochromator in the setup. Photomultiplier tube (PMT), a kind of vacuum tubes, is an extremely sensitive detector of a certain range of light (like visible light, ultra violet, etc.) The Deuterium lamp used in the experiment contains hydrogen enriched with deuterium so that both spectra can be produced simultaneously. The emission lines enter through the entrance slit, and are reflected by the collimating mirror (lateral entrance mirror) which renders them parallel and directs them to the grating. The diffraction grating diffracts the light and sends a collimated spectrum to the second mirror (lateral exit mirror) which focusses an image of the entrance slit at exit slit. Wavelength scanning through exit slit to PMT is accomplished by rotation of the grating.

Results for spectra in each Balmer series (corresponding to alpha, beta, gamma and delta for Hydrogen and Deuterium are shown below:

Where in above figures, the solid dots are the raw data form the measurement. The connecting line is the best fit for the data using the Gaussian distribution. The error bar use passion distribution to approximate.

We can use data from the best fit (fitted Gaussian function) to read the main of two peaks in each graph, which indicates the measured wavelength of Hydrogen and Deuterium in each Balmer series. Thus we can get the isotope shift to calculate the Deuteron-Proton mass ratio. Equation is indicated below:

where the delta lambda with subscript air is the measured isotope shift obtained from the experiment and A_air is a constant which can be calculated. Using the equation above, we can calculate the mass ratio in each balmer series and last calculate the weighted average. However, from the graph, we can see that as goes to higher transition order, the peaks of H and D are getting closer and the emission signal is getting weaker. Thus it becomes harder to identify two peaks; the resolution in the high order transitions is not adequate to resolve two peaks. So we place our most confident in the lower transition order (alpha), in terms of estimating the Deuteron-Proton mass ratio (as indicated at the begining of the blog post).

## Chaos

I did the LRC circuit experiment in the E&M lab last semester. I always attracted by the beautiful sine wave that generated by the function generator. I can also use the damped differential equation to get the same corresponding result. However, in the Chaos lab, due to the non-linear diode, the graph(period, peaks, etc) becomes unpredictable.

After redid the LRC circuit lab, I moved onto the chaos part. It was my first time to use this new oscilloscope, so I took some time to get myself familiar with it. After I got myself familiar with the machine, I started doing some changes. When I generated a signal with very law amplitude, zoom the screen, I can saw input 1 and 2 ‘s signals have pretty much the same period. Also, after I zooming the screen, I can saw the squiggly lines due to the diode. Since the diode only allows the signal travel in one direction, the green line never had a peak. however, we can still counted the period. As I increased the amplitude(form 20-40 kHz), I can first saw two periods within 50ms, and then I saw 4 and 6 period. However, as I kept increasing amplitude, the period is uncountable. It’s entered Chaos.

Different from the LRC circuit, we can use equation to calculate and draw corresponding graph to represent the voltage-sine wave, the chaos-circuit is unpredictable, and it will have dramatically different outcome due to a slight change of initial condition.

## Something nice

I will post my physics blog here : )