JuniorLab - User contributions [en]

Electron Diffraction

2020-02-17T22:05:11Z

Somanakuttan: /* Measuring the Planck's Constant */

== Electron diffraction experiment ==

[http://www.unm.edu/~mph/307/EDiffraction_UNM1.pdf Instructions PDF]

== Background Reading ==

== History ==

Ratio of e/m

2020-02-17T22:04:42Z

Somanakuttan: /* Measuring the Planck's Constant */

== Measuring the ratio of e/m ==

[http://www.unm.edu/~mph/307/em_UNM.pdf Instructions PDF]

== Background Reading ==

== History ==

Electron Spin Resonance

2020-02-17T22:04:14Z

Somanakuttan: Created page with "== Measuring the Electron Spin Resonance == [http://www.unm.edu/~mph/307/ESR_UNM.pdf Instructions PDF] == Background Reading == == History =="

== Measuring the Electron Spin Resonance ==

[http://www.unm.edu/~mph/307/ESR_UNM.pdf Instructions PDF]

== Background Reading ==

== History ==

Franck-Hertz

2020-02-17T22:02:59Z

Somanakuttan: Created page with "== Franck-Hertz Experiment == [http://www.unm.edu/~mph/307/FH_UNM.pdf Instructions PDF] == Background Reading == == History =="

== Franck-Hertz Experiment ==

[http://www.unm.edu/~mph/307/FH_UNM.pdf Instructions PDF]

== Background Reading ==

== History ==

Ratio of e/m

2020-02-17T22:01:46Z

Somanakuttan: Created page with "== Measuring the Planck's Constant == [http://www.unm.edu/~mph/307/em_UNM.pdf Instructions PDF] == Background Reading == == History =="

== Measuring the Planck's Constant ==

[http://www.unm.edu/~mph/307/em_UNM.pdf Instructions PDF]

== Background Reading ==

== History ==

Electron Diffraction

2020-02-17T22:00:44Z

Somanakuttan: Created page with "== Measuring the Planck's Constant == [http://www.unm.edu/~mph/307/EDiffraction_UNM1.pdf Instructions PDF] == Background Reading == == History =="

== Measuring the Planck's Constant ==

[http://www.unm.edu/~mph/307/EDiffraction_UNM1.pdf Instructions PDF]

== Background Reading ==

== History ==

Planck's Constant

2020-02-17T21:59:35Z

Somanakuttan: Created page with "== Measuring the Planck's Constant == [http://www.unm.edu/~mph/307/Planck_UNM.pdf Instructions PDF] == Background Reading == == History =="

== Measuring the Planck's Constant ==

[http://www.unm.edu/~mph/307/Planck_UNM.pdf Instructions PDF]

== Background Reading ==

== History ==

Balmer Series

2020-02-17T21:58:25Z

Somanakuttan: /* Measuring the Balmer Series */

== Measuring the Balmer Series ==

[http://www.unm.edu/~mph/307/Balmer_UNM.pdf Instructions PDF]

== Background Reading ==

== History ==

Balmer Series

2020-02-17T21:57:22Z

Somanakuttan: Created page with "== Measuring the Balmer Series == [http://www.unm.edu/~mph/307/Balmer_UNM.pdf] == Background Reading == == History =="

== Measuring the Balmer Series ==

[http://www.unm.edu/~mph/307/Balmer_UNM.pdf]

== Background Reading ==

== History ==

Compton Scattering

2020-02-03T23:09:52Z

Somanakuttan: /* Background */

==Background==
The Compton Effect (1922) demonstrates that massless photons possess momentum as well as quantized energy. Photon momentum and energy can be transferred to a stationary electron of mass m in an inelastic collision. Special relativity and quantum mechanics are essential to explain the change in frequency (equivalently wavelength) of
the scattered photon and the motion of the electron.

Compton scattering is derived using conservation of energy and momentum, where the energy and momentum of a photon of frequency ν are taken as hν and hν/c, respectively. The rest energy of the electron is mc2 and it is assumed to have zero momentum prior to its interaction with the photon.

To observe the effect, photons with energies comparable to the electron rest energy mc2 are required. The needed high energy photons are found in the gamma-ray portion of the electromagnetic spectrum. A variety of radioactive isotopes spontaneously emit the appropriate gamma-rays and are used in this experiment. Because their energy is so high, it is difficult to detect gamma-rays directly. Indirect detection is used here through a process called scintillation. A scintillator is a special material – in this case a
sodium iodide (NaI) crystal – that converts high-energy photons such as gamma-rays into visible photons that can be detected. The NaI scintillation crystal is directly attached to a photo-multiplier tube (PMT) that is sensitive enough to resolve very few visible photons. Detected photons appear as voltage pulses at the output of the PMT. The height of the voltage pulse is directly proportional to the energy of the gamma-ray that created it.

A multi-channel analyzer (MCA) measures the distribution of the PMT voltage pulses. By mapping the height of each pulse into a corresponding bin (x-axis on its display), the MCA produces a spectrum of the gamma-ray photons that strike the scintillator. The combination of scintillation, PMT, and MCA forms a gamma-ray spectrometer.
There are many possible interactions that occur when gamma-rays collide with a scintillator, but the two most relevant for this experiment are photo-electric absorption and Compton scattering. In photo-electric absorption, a gamma-ray liberates a bound electron from the scintillator crystal. This highly energetic electron travels through the NaI giving up its kinetic energy in collisions with other atoms along the path. These excitations relax back to the ground state by emitting visible photons. The more kinetic energy the electron possesses, the further it travels, the more photons are emitted, and the larger the voltage pulse at the output of the PMT. Although many visible
photons are emitted, each voltage pulse corresponds to a single gamma-ray event. The gamma-rays irradiate the scintillator at a low enough rate that they can be individually distinguished. It is important to understand that the PMT cannot detect gamma-ray photons. It only detects visible photons that result from the dissipation of kinetic energy of fast moving electrons in the scintillator.

Although multiple visible photons are produced by a single-gamma ray, the detected photon count can vary even though the gamma-ray photon energy does not change. This results in a statistical (Gaussian) distribution in the spectrometer bins. The spectrometer does not display a δ-function, but a broad peak having a width that reflects this distribution.

The primary difference between Compton scattering and photo-electric absorption is in the amount of energy transferred. In the photo-electric interaction, an electron is ionized with kinetic energy almost identical to the gamma-ray. In Compton scattering, there is a continuum of energies that can be exchanged, ranging from 0 to 100% of the incident gamma-ray energy. This arises from the angle-dependence in Equation (1). Energy is partitioned between the electron that is struck and
the scattered photon. The maximum energy an electron can acquire in Compton scattering occurs at θ = 180◦ , in which it directly recoils from a head-on collision. This produces the minimum possible scattered photon energy:

In photo-electric absorption, the MCA gives a direct measure of the gamma-ray photon energy. In Compton scattering, the MCA measures the energy of the recoiling electron, not the incident or scattered photon.

==Experiment==
The MCA x-axis is calibrated with a known radioactive source such as Cs-137. Characteristic features can be identified in the spectrum. A prominent peak at 662 keV appears
due to direct electron ionization by a Cs-137 gamma-ray. This interaction is entirely due to photoelectric absorption and produces the photo-peak. Compton scattering results in a smooth continuum of energy counts ranging from 0 eV to ∆Emax. The maximum energy from Compton scattering (the Compton edge) is due to the recoil of electrons
involved in head-on collisions. The photons emitted by these recoiling electrons must have lower energy than the photo-peak according to Equation (4). The Compton edge can be difficult to distinguish in the spectrum. It is taken as the halfway point between the rolloff shoulder and noise floor. It can be used to find the electron rest mass energy with Equation (4).

The Compton edge is associated with a minimum scattered photon energy as given by Equation (3). This backscattered photon cannot be directly detected by the PMT because its energy is too high, but it can interact with the scintillator by photo-electric absorption. The scattered photon generates a trail of electron ionization in the scintillator, the emission of many visible photons, and a prominent low energy peak in the MCA spectrum called the backscatter peak. Because this peak is produced by photo-electric absorption, the scattered gamma-ray photon energy is measured. The backscatter peak is superimposed on the Compton scattering continuum. Unlike the high-energy
photo-peak which involves no Compton scattering, the backscatter peak is from a photon produced in a head-on Compton scattering event. The energy of the backscatter peak can be used to solve for the electron rest energy through Equation (3). The Compton edge and backscatter peak provide two independent determinations of the electron
rest energy through Equations (3) and (4). Different gamma-ray sources have different energies hν resulting in different spectra and additional data.

==Equipment and Setup==

To get clean data, the PMT/scintillator and radioactive source must be shielded inside a lead brick enclosure. Use caution when moving the bricks as they are very heavy.
Radioactive sources are stored in a locked box. Ask the instructor for access. The MCA is a model UCS30 with accompanying GUI software and user manual. Referring to the
user manual will make setup and data taking easier. The most critical aspect of setup is the PMT high-voltage setting. The polarity and maximum voltage will be marked on the PMT (typically +1200V). Please have your setup confirmed by an instructor before enabling high-voltage. The MCA communicates with a host PC via USB. It biases the PMT using a special BNC cable with high voltage connectors. Never force a BNC cable onto a non-mating connector. A second BNC cable feeds the output of the PMT to the MCA, where pulses are appropriately amplified, conditioned, and counted.

Place a 1 µCi Cs-137 source next to the scintillator. You may have to experiment with its height and orientation to get the best data. Quick-start for the UCS-30 is as follows. From the menu bar, select Spectrum: Connect to Device and Mode: Pulse Height Analysis (Preamp-in). In the main menu, set the High Voltage to 600V and click the OFF button to turn the HV ON. Under Settings select Amp/HV/ADC. Set Conversion Gain at 1024; Coarse Gain: 8; Fine Gain: 1. Press the run button. You should start getting counts; adjust the HV to put the photo-peak in the approximate middle of the display. You will have to clear the display each time you make changes to the settings. When setup is adjusted to your
satisfaction, record the bin corresponding to the Cs-137 photo-peak. Keyboard arrows can help in fine positioning of the cursor. Replace the Cs-137 with the other available sources and record the bin numbers associated with their photo-peaks. Calibration data for several radioactive sources can be found in this table:
{|class=wikitable style=text align:center
|-
! Sample
! Energy
! Half life
|-
| Cs-137|| 662 keV || 30.2 yr ||
|-
| Co-60 || 1.173 MeV; 1.33 MeV || 5.3 yr ||
|-
| Na-22 || 511 keV; 1.275 MeV || 2.6 yr||
|-
| Ba-133|| 356 keV || 10.5 yr ||
|-
| Mn-54 || 835 keV || 303 day ||
|-
| Cd-109 || 88 keV || 453 day ||
|-
| Co-57 || 122 keV || 270 day ||
|}

You may also get sum peaks at higher energies. Plot the photo-peak energy vs the bin number and attempt to make a linear, least-squares fit. This line will be your calibration curve; do not use the auto-calibrate function of the spectrometer. Replace the Cs-137 source and measure the full-width, half-maximum of the photo-peak. Report
this value in energy using the calibration curve.

Measure the Compton edge and backscatter peak for as many sources as possible. Use these to calculate the electron rest energy and rest mass. Be sure to include the uncertainties in your reported values.

Is the half-height energy the best estimate for the Compton edge? Which of the two peaks produce
better results and why?

Why do backscatter photons produce a peak instead of a much broader continuum?

Compton Scattering

2020-02-03T23:09:06Z

Somanakuttan: /* Equipment and Setup */

==Background==
The Compton Effect (1922) demonstrates that massless photons possess momentum as well as quantized energy. Photon momentum and energy can be transferred to a stationary electron of mass m in an inelastic collision. Special relativity and quantum mechanics are essential to explain the change in frequency (equivalently wavelength) of
the scattered photon and the motion of the electron.

Compton scattering is derived using conservation of energy and momentum, where the energy and momentum of a photon of frequency ν are taken as hν and hν/c, respectively. The rest energy of the electron is mc2 and it is assumed to have zero momentum prior to its interaction with the photon

To observe the effect, photons with energies comparable to the electron rest energy mc2 are required. The needed high energy photons are found in the gamma-ray portion of the electromagnetic spectrum. A variety of radioactive isotopes spontaneously emit the appropriate gamma-rays and are used in this experiment. Because their energy is so high, it is difficult to detect gamma-rays directly. Indirect detection is used here through a process called scintillation. A scintillator is a special material – in this case a
sodium iodide (NaI) crystal – that converts high-energy photons such as gamma-rays into visible photons that can be detected. The NaI scintillation crystal is directly attached to a photo-multiplier tube (PMT) that is sensitive enough to resolve very few visible photons. Detected photons appear as voltage pulses at the output of the PMT. The height of the voltage pulse is directly proportional to the energy of the gamma-ray that created it.

A multi-channel analyzer (MCA) measures the distribution of the PMT voltage pulses. By mapping the height of each pulse into a corresponding bin (x-axis on its display), the MCA produces a spectrum of the gamma-ray photons that strike the scintillator. The combination of scintillation, PMT, and MCA forms a gamma-ray spectrometer.
There are many possible interactions that occur when gamma-rays collide with a scintillator, but the two most relevant for this experiment are photo-electric absorption and Compton scattering. In photo-electric absorption, a gamma-ray liberates a bound electron from the scintillator crystal. This highly energetic electron travels through the NaI giving up its kinetic energy in collisions with other atoms along the path. These excitations relax back to the ground state by emitting visible photons. The more kinetic energy the electron possesses, the further it travels, the more photons are emitted, and the larger the voltage pulse at the output of the PMT. Although many visible
photons are emitted, each voltage pulse corresponds to a single gamma-ray event. The gamma-rays irradiate the scintillator at a low enough rate that they can be individually distinguished. It is important to understand that the PMT cannot detect gamma-ray photons. It only detects visible photons that result from the dissipation of kinetic energy of fast moving electrons in the scintillator.

Although multiple visible photons are produced by a single-gamma ray, the detected photon count can vary even though the gamma-ray photon energy does not change. This results in a statistical (Gaussian) distribution in the spectrometer bins. The spectrometer does not display a δ-function, but a broad peak having a width that reflects this distribution.

The primary difference between Compton scattering and photo-electric absorption is in the amount of energy transferred. In the photo-electric interaction, an electron is ionized with kinetic energy almost identical to the gamma-ray. In Compton scattering, there is a continuum of energies that can be exchanged, ranging from 0 to 100% of the incident gamma-ray energy. This arises from the angle-dependence in Equation (1). Energy is partitioned between the electron that is struck and
the scattered photon. The maximum energy an electron can acquire in Compton scattering occurs at θ = 180◦ , in which it directly recoils from a head-on collision. This produces the minimum possible scattered photon energy:

In photo-electric absorption, the MCA gives a direct measure of the gamma-ray photon energy. In Compton scattering, the MCA measures the energy of the recoiling electron, not the incident or scattered photon.

==Experiment==
The MCA x-axis is calibrated with a known radioactive source such as Cs-137. Characteristic features can be identified in the spectrum. A prominent peak at 662 keV appears
due to direct electron ionization by a Cs-137 gamma-ray. This interaction is entirely due to photoelectric absorption and produces the photo-peak. Compton scattering results in a smooth continuum of energy counts ranging from 0 eV to ∆Emax. The maximum energy from Compton scattering (the Compton edge) is due to the recoil of electrons
involved in head-on collisions. The photons emitted by these recoiling electrons must have lower energy than the photo-peak according to Equation (4). The Compton edge can be difficult to distinguish in the spectrum. It is taken as the halfway point between the rolloff shoulder and noise floor. It can be used to find the electron rest mass energy with Equation (4).

The Compton edge is associated with a minimum scattered photon energy as given by Equation (3). This backscattered photon cannot be directly detected by the PMT because its energy is too high, but it can interact with the scintillator by photo-electric absorption. The scattered photon generates a trail of electron ionization in the scintillator, the emission of many visible photons, and a prominent low energy peak in the MCA spectrum called the backscatter peak. Because this peak is produced by photo-electric absorption, the scattered gamma-ray photon energy is measured. The backscatter peak is superimposed on the Compton scattering continuum. Unlike the high-energy
photo-peak which involves no Compton scattering, the backscatter peak is from a photon produced in a head-on Compton scattering event. The energy of the backscatter peak can be used to solve for the electron rest energy through Equation (3). The Compton edge and backscatter peak provide two independent determinations of the electron
rest energy through Equations (3) and (4). Different gamma-ray sources have different energies hν resulting in different spectra and additional data.

==Equipment and Setup==

To get clean data, the PMT/scintillator and radioactive source must be shielded inside a lead brick enclosure. Use caution when moving the bricks as they are very heavy.
Radioactive sources are stored in a locked box. Ask the instructor for access. The MCA is a model UCS30 with accompanying GUI software and user manual. Referring to the
user manual will make setup and data taking easier. The most critical aspect of setup is the PMT high-voltage setting. The polarity and maximum voltage will be marked on the PMT (typically +1200V). Please have your setup confirmed by an instructor before enabling high-voltage. The MCA communicates with a host PC via USB. It biases the PMT using a special BNC cable with high voltage connectors. Never force a BNC cable onto a non-mating connector. A second BNC cable feeds the output of the PMT to the MCA, where pulses are appropriately amplified, conditioned, and counted.

Place a 1 µCi Cs-137 source next to the scintillator. You may have to experiment with its height and orientation to get the best data. Quick-start for the UCS-30 is as follows. From the menu bar, select Spectrum: Connect to Device and Mode: Pulse Height Analysis (Preamp-in). In the main menu, set the High Voltage to 600V and click the OFF button to turn the HV ON. Under Settings select Amp/HV/ADC. Set Conversion Gain at 1024; Coarse Gain: 8; Fine Gain: 1. Press the run button. You should start getting counts; adjust the HV to put the photo-peak in the approximate middle of the display. You will have to clear the display each time you make changes to the settings. When setup is adjusted to your
satisfaction, record the bin corresponding to the Cs-137 photo-peak. Keyboard arrows can help in fine positioning of the cursor. Replace the Cs-137 with the other available sources and record the bin numbers associated with their photo-peaks. Calibration data for several radioactive sources can be found in this table:
{|class=wikitable style=text align:center
|-
! Sample
! Energy
! Half life
|-
| Cs-137|| 662 keV || 30.2 yr ||
|-
| Co-60 || 1.173 MeV; 1.33 MeV || 5.3 yr ||
|-
| Na-22 || 511 keV; 1.275 MeV || 2.6 yr||
|-
| Ba-133|| 356 keV || 10.5 yr ||
|-
| Mn-54 || 835 keV || 303 day ||
|-
| Cd-109 || 88 keV || 453 day ||
|-
| Co-57 || 122 keV || 270 day ||
|}

You may also get sum peaks at higher energies. Plot the photo-peak energy vs the bin number and attempt to make a linear, least-squares fit. This line will be your calibration curve; do not use the auto-calibrate function of the spectrometer. Replace the Cs-137 source and measure the full-width, half-maximum of the photo-peak. Report
this value in energy using the calibration curve.

Measure the Compton edge and backscatter peak for as many sources as possible. Use these to calculate the electron rest energy and rest mass. Be sure to include the uncertainties in your reported values.

Is the half-height energy the best estimate for the Compton edge? Which of the two peaks produce
better results and why?

Why do backscatter photons produce a peak instead of a much broader continuum?

Compton Scattering

2020-02-03T22:49:23Z

Somanakuttan: /* Equipment and Setup */

==Background==
The Compton Effect (1922) demonstrates that massless photons possess momentum as well as quantized energy. Photon momentum and energy can be transferred to a stationary electron of mass m in an inelastic collision. Special relativity and quantum mechanics are essential to explain the change in frequency (equivalently wavelength) of
the scattered photon and the motion of the electron.

Compton scattering is derived using conservation of energy and momentum, where the energy and momentum of a photon of frequency ν are taken as hν and hν/c, respectively. The rest energy of the electron is mc2 and it is assumed to have zero momentum prior to its interaction with the photon

To observe the effect, photons with energies comparable to the electron rest energy mc2 are required. The needed high energy photons are found in the gamma-ray portion of the electromagnetic spectrum. A variety of radioactive isotopes spontaneously emit the appropriate gamma-rays and are used in this experiment. Because their energy is so high, it is difficult to detect gamma-rays directly. Indirect detection is used here through a process called scintillation. A scintillator is a special material – in this case a
sodium iodide (NaI) crystal – that converts high-energy photons such as gamma-rays into visible photons that can be detected. The NaI scintillation crystal is directly attached to a photo-multiplier tube (PMT) that is sensitive enough to resolve very few visible photons. Detected photons appear as voltage pulses at the output of the PMT. The height of the voltage pulse is directly proportional to the energy of the gamma-ray that created it.

A multi-channel analyzer (MCA) measures the distribution of the PMT voltage pulses. By mapping the height of each pulse into a corresponding bin (x-axis on its display), the MCA produces a spectrum of the gamma-ray photons that strike the scintillator. The combination of scintillation, PMT, and MCA forms a gamma-ray spectrometer.
There are many possible interactions that occur when gamma-rays collide with a scintillator, but the two most relevant for this experiment are photo-electric absorption and Compton scattering. In photo-electric absorption, a gamma-ray liberates a bound electron from the scintillator crystal. This highly energetic electron travels through the NaI giving up its kinetic energy in collisions with other atoms along the path. These excitations relax back to the ground state by emitting visible photons. The more kinetic energy the electron possesses, the further it travels, the more photons are emitted, and the larger the voltage pulse at the output of the PMT. Although many visible
photons are emitted, each voltage pulse corresponds to a single gamma-ray event. The gamma-rays irradiate the scintillator at a low enough rate that they can be individually distinguished. It is important to understand that the PMT cannot detect gamma-ray photons. It only detects visible photons that result from the dissipation of kinetic energy of fast moving electrons in the scintillator.

Although multiple visible photons are produced by a single-gamma ray, the detected photon count can vary even though the gamma-ray photon energy does not change. This results in a statistical (Gaussian) distribution in the spectrometer bins. The spectrometer does not display a δ-function, but a broad peak having a width that reflects this distribution.

The primary difference between Compton scattering and photo-electric absorption is in the amount of energy transferred. In the photo-electric interaction, an electron is ionized with kinetic energy almost identical to the gamma-ray. In Compton scattering, there is a continuum of energies that can be exchanged, ranging from 0 to 100% of the incident gamma-ray energy. This arises from the angle-dependence in Equation (1). Energy is partitioned between the electron that is struck and
the scattered photon. The maximum energy an electron can acquire in Compton scattering occurs at θ = 180◦ , in which it directly recoils from a head-on collision. This produces the minimum possible scattered photon energy:

In photo-electric absorption, the MCA gives a direct measure of the gamma-ray photon energy. In Compton scattering, the MCA measures the energy of the recoiling electron, not the incident or scattered photon.

==Experiment==
The MCA x-axis is calibrated with a known radioactive source such as Cs-137. Characteristic features can be identified in the spectrum. A prominent peak at 662 keV appears
due to direct electron ionization by a Cs-137 gamma-ray. This interaction is entirely due to photoelectric absorption and produces the photo-peak. Compton scattering results in a smooth continuum of energy counts ranging from 0 eV to ∆Emax. The maximum energy from Compton scattering (the Compton edge) is due to the recoil of electrons
involved in head-on collisions. The photons emitted by these recoiling electrons must have lower energy than the photo-peak according to Equation (4). The Compton edge can be difficult to distinguish in the spectrum. It is taken as the halfway point between the rolloff shoulder and noise floor. It can be used to find the electron rest mass energy with Equation (4).

The Compton edge is associated with a minimum scattered photon energy as given by Equation (3). This backscattered photon cannot be directly detected by the PMT because its energy is too high, but it can interact with the scintillator by photo-electric absorption. The scattered photon generates a trail of electron ionization in the scintillator, the emission of many visible photons, and a prominent low energy peak in the MCA spectrum called the backscatter peak. Because this peak is produced by photo-electric absorption, the scattered gamma-ray photon energy is measured. The backscatter peak is superimposed on the Compton scattering continuum. Unlike the high-energy
photo-peak which involves no Compton scattering, the backscatter peak is from a photon produced in a head-on Compton scattering event. The energy of the backscatter peak can be used to solve for the electron rest energy through Equation (3). The Compton edge and backscatter peak provide two independent determinations of the electron
rest energy through Equations (3) and (4). Different gamma-ray sources have different energies hν resulting in different spectra and additional data.

==Equipment and Setup==

To get clean data, the PMT/scintillator and radioactive source must be shielded inside a lead brick enclosure. Use caution when moving the bricks as they are very heavy.
Radioactive sources are stored in a locked box. Ask the instructor for access. The MCA is a model UCS30 with accompanying GUI software and user manual. Referring to the
user manual will make setup and data taking easier. The most critical aspect of setup is the PMT high-voltage setting. The polarity and maximum voltage will be marked on the PMT (typically +1200V). Please have your setup confirmed by an instructor before enabling high-voltage. The MCA communicates with a host PC via USB. It biases the PMT using a special BNC cable with high voltage connectors. Never force a BNC cable onto a non-mating connector. A second BNC cable feeds the output of the PMT to the MCA, where pulses are appropriately amplified, conditioned, and counted.

Place a 1 µCi Cs-137 source next to the scintillator. You may have to experiment with its height and orientation to get the best data. Quick-start for the UCS-30 is as follows. From the menu bar, select Spectrum: Connect to Device and Mode: Pulse Height Analysis (Preamp-in). In the main menu, set the High Voltage to 600V and click the OFF button to turn the HV ON. Under Settings select Amp/HV/ADC. Set Conversion Gain at 1024; Coarse Gain: 8; Fine Gain: 1. Press the run button. You should start getting counts; adjust the HV to put the photo-peak in the approximate middle of the display. You will have to clear the display each time you make changes to the settings. When setup is adjusted to your
satisfaction, record the bin corresponding to the Cs-137 photo-peak. Keyboard arrows can help in fine positioning of the cursor. Replace the Cs-137 with the other available sources and record the bin numbers associated with their photo-peaks. Calibration data for several radioactive sources can be found in this table:
{| class="wikitable"

|-
| Cs-137|| 662 keV || 30.2 yr half-life ||
|-
| Co-60 || 1.173 MeV; 1.33 MeV || 5.3 yr half-life ||
|-
| Na-22 || 511 keV; 1.275 MeV || 2.6 yr half-life ||
|-
| Ba-133|| 356 keV || 10.5 yr half-life ||
|-
| Mn-54 || 835 keV || 303 day half-life ||
|-
| Cd-109 || 88 keV || 453 day half-life ||
|-
| Co-57 || 122 keV || 270 day half-life||
|-

You may also get sum peaks at higher energies. Plot the photo-peak energy vs the bin number and attempt to make a linear, least-squares fit. This line will be your calibration curve; do not use the auto-calibrate function of the spectrometer. Replace the Cs-137 source and measure the full-width, half-maximum of the photo-peak. Report
this value in energy using the calibration curve.

Measure the Compton edge and backscatter peak for as many sources as possible. Use these to calculate the electron rest energy and rest mass. Be sure to include the uncertainties in your reported values.

Is the half-height energy the best estimate for the Compton edge? Which of the two peaks produce
better results and why?

Why do backscatter photons produce a peak instead of a much broader continuum?

Compton Scattering

2020-02-03T22:44:03Z

Somanakuttan: /* Background */

==Background==
The Compton Effect (1922) demonstrates that massless photons possess momentum as well as quantized energy. Photon momentum and energy can be transferred to a stationary electron of mass m in an inelastic collision. Special relativity and quantum mechanics are essential to explain the change in frequency (equivalently wavelength) of
the scattered photon and the motion of the electron.

Compton scattering is derived using conservation of energy and momentum, where the energy and momentum of a photon of frequency ν are taken as hν and hν/c, respectively. The rest energy of the electron is mc2 and it is assumed to have zero momentum prior to its interaction with the photon

To observe the effect, photons with energies comparable to the electron rest energy mc2 are required. The needed high energy photons are found in the gamma-ray portion of the electromagnetic spectrum. A variety of radioactive isotopes spontaneously emit the appropriate gamma-rays and are used in this experiment. Because their energy is so high, it is difficult to detect gamma-rays directly. Indirect detection is used here through a process called scintillation. A scintillator is a special material – in this case a
sodium iodide (NaI) crystal – that converts high-energy photons such as gamma-rays into visible photons that can be detected. The NaI scintillation crystal is directly attached to a photo-multiplier tube (PMT) that is sensitive enough to resolve very few visible photons. Detected photons appear as voltage pulses at the output of the PMT. The height of the voltage pulse is directly proportional to the energy of the gamma-ray that created it.

A multi-channel analyzer (MCA) measures the distribution of the PMT voltage pulses. By mapping the height of each pulse into a corresponding bin (x-axis on its display), the MCA produces a spectrum of the gamma-ray photons that strike the scintillator. The combination of scintillation, PMT, and MCA forms a gamma-ray spectrometer.
There are many possible interactions that occur when gamma-rays collide with a scintillator, but the two most relevant for this experiment are photo-electric absorption and Compton scattering. In photo-electric absorption, a gamma-ray liberates a bound electron from the scintillator crystal. This highly energetic electron travels through the NaI giving up its kinetic energy in collisions with other atoms along the path. These excitations relax back to the ground state by emitting visible photons. The more kinetic energy the electron possesses, the further it travels, the more photons are emitted, and the larger the voltage pulse at the output of the PMT. Although many visible
photons are emitted, each voltage pulse corresponds to a single gamma-ray event. The gamma-rays irradiate the scintillator at a low enough rate that they can be individually distinguished. It is important to understand that the PMT cannot detect gamma-ray photons. It only detects visible photons that result from the dissipation of kinetic energy of fast moving electrons in the scintillator.

Although multiple visible photons are produced by a single-gamma ray, the detected photon count can vary even though the gamma-ray photon energy does not change. This results in a statistical (Gaussian) distribution in the spectrometer bins. The spectrometer does not display a δ-function, but a broad peak having a width that reflects this distribution.

The primary difference between Compton scattering and photo-electric absorption is in the amount of energy transferred. In the photo-electric interaction, an electron is ionized with kinetic energy almost identical to the gamma-ray. In Compton scattering, there is a continuum of energies that can be exchanged, ranging from 0 to 100% of the incident gamma-ray energy. This arises from the angle-dependence in Equation (1). Energy is partitioned between the electron that is struck and
the scattered photon. The maximum energy an electron can acquire in Compton scattering occurs at θ = 180◦ , in which it directly recoils from a head-on collision. This produces the minimum possible scattered photon energy:

In photo-electric absorption, the MCA gives a direct measure of the gamma-ray photon energy. In Compton scattering, the MCA measures the energy of the recoiling electron, not the incident or scattered photon.

==Experiment==
The MCA x-axis is calibrated with a known radioactive source such as Cs-137. Characteristic features can be identified in the spectrum. A prominent peak at 662 keV appears
due to direct electron ionization by a Cs-137 gamma-ray. This interaction is entirely due to photoelectric absorption and produces the photo-peak. Compton scattering results in a smooth continuum of energy counts ranging from 0 eV to ∆Emax. The maximum energy from Compton scattering (the Compton edge) is due to the recoil of electrons
involved in head-on collisions. The photons emitted by these recoiling electrons must have lower energy than the photo-peak according to Equation (4). The Compton edge can be difficult to distinguish in the spectrum. It is taken as the halfway point between the rolloff shoulder and noise floor. It can be used to find the electron rest mass energy with Equation (4).

The Compton edge is associated with a minimum scattered photon energy as given by Equation (3). This backscattered photon cannot be directly detected by the PMT because its energy is too high, but it can interact with the scintillator by photo-electric absorption. The scattered photon generates a trail of electron ionization in the scintillator, the emission of many visible photons, and a prominent low energy peak in the MCA spectrum called the backscatter peak. Because this peak is produced by photo-electric absorption, the scattered gamma-ray photon energy is measured. The backscatter peak is superimposed on the Compton scattering continuum. Unlike the high-energy
photo-peak which involves no Compton scattering, the backscatter peak is from a photon produced in a head-on Compton scattering event. The energy of the backscatter peak can be used to solve for the electron rest energy through Equation (3). The Compton edge and backscatter peak provide two independent determinations of the electron
rest energy through Equations (3) and (4). Different gamma-ray sources have different energies hν resulting in different spectra and additional data.

==Equipment and Setup==

To get clean data, the PMT/scintillator and radioactive source must be shielded inside a lead brick enclosure. Use caution when moving the bricks as they are very heavy.
Radioactive sources are stored in a locked box. Ask the instructor for access. The MCA is a model UCS30 with accompanying GUI software and user manual. Referring to the
user manual will make setup and data taking easier. The most critical aspect of setup is the PMT high-voltage setting. The polarity and maximum voltage will be marked on the PMT (typically +1200V). Please have your setup confirmed by an instructor before enabling high-voltage. The MCA communicates with a host PC via USB. It biases the PMT using a special BNC cable with high voltage connectors. Never force a BNC cable onto a non-mating connector. A second BNC cable feeds the output of the PMT to the MCA, where pulses are appropriately amplified, conditioned, and counted.

Place a 1 µCi Cs-137 source next to the scintillator. You may have to experiment with its height and orientation to get the best data. Quick-start for the UCS-30 is as follows. From the menu bar, select Spectrum: Connect to Device and Mode: Pulse Height Analysis (Preamp-in). In the main menu, set the High Voltage to 600V and click the OFF button to turn the HV ON. Under Settings select Amp/HV/ADC. Set Conversion Gain at 1024; Coarse Gain: 8; Fine Gain: 1. Press the run button. You should start getting counts; adjust the HV to put the photo-peak in the approximate middle of the display. You will have to clear the display each time you make changes to the settings. When setup is adjusted to your
satisfaction, record the bin corresponding to the Cs-137 photo-peak. Keyboard arrows can help in fine positioning of the cursor. Replace the Cs-137 with the other available sources and record the bin numbers associated with their photo-peaks. Calibration data for several radioactive sources can be found in this table:
{| class="wikitable"

|-
| Speed of Light || No || Yes ||
|-
| Acoustic Wave Propagation || Yes || No ||
|-
| Balmer Series || No || No ||
|-
| Poisson Statistics || Yes || No ||
|-
| Planck's Constant || No || No ||
|-
| Compton Scattering || Yes || No ||
|-
| Electron Diffraction || No || No ||
|-

Compton Scattering

2020-02-03T22:32:27Z

Somanakuttan: /* Background */

Compton Scattering

2020-02-03T22:30:19Z

Somanakuttan: /* Background */

Compton Scattering

2020-02-03T22:27:16Z

Somanakuttan: Created page with "==Background== The Compton Effect (1922) demonstrates that massless photons possess momentum as well as quantized energy. Photon momentum and energy can be transferred to a st..."

Poisson Statistics

2020-02-03T22:16:28Z

Somanakuttan: /* Analysis */

== Background ==

The Poisson distribution can characterize random events that occur at a well-defined average rate. It is widely used in atomic and sub-atomic physics. The Poisson distribution is effective in a variety of statistical applications. The most common involve event probabilities, but several assumptions must hold true: i) the rate at which random events
occur does not change for the duration of the measurement; ii) the occurrence of one event does not change the likelihood of another event; iii) events occur at a slow enough rate that they can be individually distinguished.

In this experiment, Poisson statistics will be used to analyze random radioactive decay events that occur in a defined time interval. A decay occurs an integer k number of times in the interval, including possibly not at all (k = 0). The average number of events expected in a defined time interval is λ, known as the event rate. Given λ,
the probability of observing k events in the time interval is:

If the interval gets longer, λ increases commensurately and Pk changes.

[http://www.unm.edu/~mph/307/Poisson_UNM2.pdf Experiment Instructions (pdf)]

==Experiment==
The radioactive source is Cs-137, with half-life of 30.2 years. The probability that a single atom will decay in a 100 ms interval, for example, is 6.87 × 10−11, i.e. an
extremely unlikely occurrence. If the source has enough mass, however, a sufficient number of decays will happen in reasonable measurement time. Because their energy is so high, it is difficult to detect gamma-rays directly. Indirect detection is used here through a process called scintillation. A scintillator is a special material – in this
case a sodium iodide (NaI) crystal – that converts high-energy photons such as gamma-rays into visible photons that can be detected. The NaI scintillation crystal is directly attached to a photo-multiplier tube (PMT) that is sensitive enough to resolve very few visible photons. Detected photons appear as voltage pulses at the output of the PMT. The height of the voltage pulse is directly proportional to the energy of the gamma-ray that created it, which is 662 keV for Cs-137.

A multi-channel analyzer (MCA) can measure the energy of the gamma-rays and also the rate at which they strike the scintillator. The rate of spontaneous gamma-ray emission is of interest in this experiment. The MCA is configured to count gamma-rays in a defined time interval. It does this counting repetitively, building up a statistical ensemble of N intervals each holding an event count. When viewed as a histogram, a distinct distribution becomes evident. The key to observing a Poisson distribution is keeping the event rate λ sufficiently low. The distribution plot will appear asymmetric. As λ increases, the distribution transitions to a symmetric Gaussian.

==Equipment and Setup.==
The PMT/scintillator and radioactive source must be shielded inside a lead brick enclosure. Use caution when moving the bricks as they are very heavy. Radioactive sources are stored in a locked box. Ask the instructor for access. The MCA is a model UCS30 with accompanying GUI software and user manual. Referring to the user manual will make setup and data taking easier. The most critical aspect of the setup is the PMT high-voltage setting. The polarity and maximum voltage will be marked on the PMT (typically +1200V). Please have your setup confirmed by an instructor before enabling high-voltage.

Initial data is acquired without a radioactive source. Place the PMT/scintillator inside the lead brick enclosure and proceed to the MCA setup. The MCA communicates with a host PC via USB. It biases the PMT using a special BNC cable with high voltage connectors. Never force a BNC cable onto a non-mating connector. A second BNC cable feeds the output of the PMT to the MCA, where pulses are appropriately amplified, conditioned, and counted. Quick-start for the UCS-30 is as follows. From the menu bar, select Spectrum: Connect to Device, then Mode: Pulse Height Analysis (Preamp-in). In the main menu, set the High Voltage to 1000V and click the OFF button to turn the HV ON. Under Settings select
Amp/HV/ADC. Set Conversion Gain at 256; Coarse Gain: 1; Fine Gain: 1. Make sure the discriminator range is at maximum: 3–256. Switch to Mode: MCS Internal. The duration of the acquisition interval is set with Settings: MCS Settings: Dwell Time. The combination of the adjustable PMT voltage (i.e. gain) and dwell time will determine the event rate. The MCA acquires counts in a succession of N = 256 measurement intervals. Press the run button. Counts will be displayed for each interval. This should be a relatively
flat line, but with statistical fluctuations. You will need to make 3 data runs to attain 3 different average event rates in each interval: i) 1–2 counts, ii) 5 counts, and iii) 10 counts. At the lowest event rate, there will be many empty intervals. At the highest, there will likely be none. To get the needed count rates, perform trial-and-error experimentation with the PMT voltage and dwell time. When an acceptable data run has been completed, save it to disk as a tab or comma delineated file. In your writeup, discuss why counts would be present in the absence of a radioactive source.

Place a 1 µCi Cs-137 source next to the scintillator. Set Mode: Pulse Height Analysis(Preamp-in). In the main menu, set the High Voltage. This is not critical; 1000V is a good
initial setting. Under Settings select Amp/HV/ADC. Set Conversion Gain at 256; Coarse Gain: 4; Fine Gain: 1. Click the OFF button to turn the HV ON. Press the run button, let
counts accumulate, and identify the prominent photo-peak. This peak corresponds to the 662 keV gamma-ray of Cs-137. The combination of high-voltage and gain determines where
the peak appears in the MCA display. If these values are too high, the rate of gamma-ray detection will be too rapid to observe Poisson statistics. Adjust the discriminator high and low channel settings to bracket this peak. This can be done from the menu or by sliding the two triangles below the x-axis. Note: This is not the same as setting the ROI. Switch to Mode: MCS Internal. The voltage and gain should no longer be adjusted to change the event rate since the discriminator levels will no longer be correct. The rate can be modified with the dwell time as before and also by changing the distance between the Cs-137 source and scintillator. If the voltage/gain must be changed to get an acceptable event rate, the discriminator will also have to be reset in the PHA mode. Make 3 data runs as before to attain 3 different average event rates in each interval: i) 1–2 counts, ii) 5 counts, and iii) 10 counts. Save data to disk as a tab or comma delineated file.

==Analysis==
Using software of your choice, plot a histogram for each of your 6 data sets. Make sure the x-axis bins are configured for integer counts. For sufficiently low event rates, the
plotted distribution should be asymmetric and skewed towards the origin, consistent with Poisson statistics. There are statistical fluctuations associated with this measurement. These are distinguished from fluctuations due to instrumental uncertainty, for example, variation of the MCA measurement intervals. The statistical error can be obtained by doing this measurement repeatedly, but it is much easier to realize that the count in each histogram bin originates from random events. If Ck is the count in the kth bin, the uncertainty can be represented by the standard deviation σk associated with Poisson statistics: σk = √Ck. This is an important feature of Poisson statistics compared to a Gaussian distribution. In the latter, the standard deviation must be determined independently. Add statistical error bars σk to each point of
your histogram.

To generate a theoretical curve, the average event rate λ is required. This should be calculated for each data set. This is not simply using the approximate target rates of 1–2, 5, 10 counts/interval, although the target rate may be similar to λ. A precise number for λ must be obtained from the data. With Equation (1), the total number of event intervals N, and the extracted value of λ, a Poisson curve can be generated and compared to the experimental result. The standard deviation of the distribution is σ =
√ λ . How does the average event rate λ ± σ compare to the counts Ck in the N individual intervals? Can you quantify how well this rate describes what was measured in the ensemble
of intervals? The quality or “goodness” of the Poisson curve in describing the distribution is quantified with the parameter χ2 . If there are n bins in the histogram, then

This characterizes the difference between experiment (Ck) and theory (PkN) at each point 3 on the histogram (numerator) and the expected spread (denominator). χ2 = 0 represents
perfect agreement, but this should not happen with a statistical ensemble. Intuitively, we expect that experimental and theoretical deviations to be about the same, i.e. χ
2 ≈ n. The expectation value is reduced by the number of degrees of freedom, which is one in this case, leading to: hχ 2 i = n − 1. Perform this analysis on your data and compare to the expected result. Further discussion can be found in the textbook by Bevington and Robinson on data reduction and error analysis.

At higher event rates, the histograms become more symmetric and are better described by a Gaussian distribution:

Evaluate Eq. (3) for the three data sets without Cs-137. The Gaussian curves G can be compared to the Poisson curves P that were obtained from Eq. (1). To do this, normalize
both curves, then calculate and plot the difference curve: (G − P)/P. Compare by plotting this curve together with the predicted result Tk:

where δ = k − λ. This provides a clear visualization of the asymmetry. More information
can be found in the 1975 paper by L.J. Curtis on the class website.

== Background Reading ==

[https://www.umass.edu/wsp/archive/reference/poisson/index.html The Poisson Distribution]

== History ==

Experiment set up and verified by Martin Hoeferkamp, January 2020

Poisson Statistics

2020-02-03T22:13:11Z

Somanakuttan:

== Background ==

The Poisson distribution can characterize random events that occur at a well-defined average rate. It is widely used in atomic and sub-atomic physics. The Poisson distribution is effective in a variety of statistical applications. The most common involve event probabilities, but several assumptions must hold true: i) the rate at which random events
occur does not change for the duration of the measurement; ii) the occurrence of one event does not change the likelihood of another event; iii) events occur at a slow enough rate that they can be individually distinguished.

In this experiment, Poisson statistics will be used to analyze random radioactive decay events that occur in a defined time interval. A decay occurs an integer k number of times in the interval, including possibly not at all (k = 0). The average number of events expected in a defined time interval is λ, known as the event rate. Given λ,
the probability of observing k events in the time interval is:

If the interval gets longer, λ increases commensurately and Pk changes.

[http://www.unm.edu/~mph/307/Poisson_UNM2.pdf Experiment Instructions (pdf)]

==Experiment==
The radioactive source is Cs-137, with half-life of 30.2 years. The probability that a single atom will decay in a 100 ms interval, for example, is 6.87 × 10−11, i.e. an
extremely unlikely occurrence. If the source has enough mass, however, a sufficient number of decays will happen in reasonable measurement time. Because their energy is so high, it is difficult to detect gamma-rays directly. Indirect detection is used here through a process called scintillation. A scintillator is a special material – in this
case a sodium iodide (NaI) crystal – that converts high-energy photons such as gamma-rays into visible photons that can be detected. The NaI scintillation crystal is directly attached to a photo-multiplier tube (PMT) that is sensitive enough to resolve very few visible photons. Detected photons appear as voltage pulses at the output of the PMT. The height of the voltage pulse is directly proportional to the energy of the gamma-ray that created it, which is 662 keV for Cs-137.

A multi-channel analyzer (MCA) can measure the energy of the gamma-rays and also the rate at which they strike the scintillator. The rate of spontaneous gamma-ray emission is of interest in this experiment. The MCA is configured to count gamma-rays in a defined time interval. It does this counting repetitively, building up a statistical ensemble of N intervals each holding an event count. When viewed as a histogram, a distinct distribution becomes evident. The key to observing a Poisson distribution is keeping the event rate λ sufficiently low. The distribution plot will appear asymmetric. As λ increases, the distribution transitions to a symmetric Gaussian.

==Equipment and Setup.==
The PMT/scintillator and radioactive source must be shielded inside a lead brick enclosure. Use caution when moving the bricks as they are very heavy. Radioactive sources are stored in a locked box. Ask the instructor for access. The MCA is a model UCS30 with accompanying GUI software and user manual. Referring to the user manual will make setup and data taking easier. The most critical aspect of the setup is the PMT high-voltage setting. The polarity and maximum voltage will be marked on the PMT (typically +1200V). Please have your setup confirmed by an instructor before enabling high-voltage.

Initial data is acquired without a radioactive source. Place the PMT/scintillator inside the lead brick enclosure and proceed to the MCA setup. The MCA communicates with a host PC via USB. It biases the PMT using a special BNC cable with high voltage connectors. Never force a BNC cable onto a non-mating connector. A second BNC cable feeds the output of the PMT to the MCA, where pulses are appropriately amplified, conditioned, and counted. Quick-start for the UCS-30 is as follows. From the menu bar, select Spectrum: Connect to Device, then Mode: Pulse Height Analysis (Preamp-in). In the main menu, set the High Voltage to 1000V and click the OFF button to turn the HV ON. Under Settings select
Amp/HV/ADC. Set Conversion Gain at 256; Coarse Gain: 1; Fine Gain: 1. Make sure the discriminator range is at maximum: 3–256. Switch to Mode: MCS Internal. The duration of the acquisition interval is set with Settings: MCS Settings: Dwell Time. The combination of the adjustable PMT voltage (i.e. gain) and dwell time will determine the event rate. The MCA acquires counts in a succession of N = 256 measurement intervals. Press the run button. Counts will be displayed for each interval. This should be a relatively
flat line, but with statistical fluctuations. You will need to make 3 data runs to attain 3 different average event rates in each interval: i) 1–2 counts, ii) 5 counts, and iii) 10 counts. At the lowest event rate, there will be many empty intervals. At the highest, there will likely be none. To get the needed count rates, perform trial-and-error experimentation with the PMT voltage and dwell time. When an acceptable data run has been completed, save it to disk as a tab or comma delineated file. In your writeup, discuss why counts would be present in the absence of a radioactive source.

Place a 1 µCi Cs-137 source next to the scintillator. Set Mode: Pulse Height Analysis(Preamp-in). In the main menu, set the High Voltage. This is not critical; 1000V is a good
initial setting. Under Settings select Amp/HV/ADC. Set Conversion Gain at 256; Coarse Gain: 4; Fine Gain: 1. Click the OFF button to turn the HV ON. Press the run button, let
counts accumulate, and identify the prominent photo-peak. This peak corresponds to the 662 keV gamma-ray of Cs-137. The combination of high-voltage and gain determines where
the peak appears in the MCA display. If these values are too high, the rate of gamma-ray detection will be too rapid to observe Poisson statistics. Adjust the discriminator high and low channel settings to bracket this peak. This can be done from the menu or by sliding the two triangles below the x-axis. Note: This is not the same as setting the ROI. Switch to Mode: MCS Internal. The voltage and gain should no longer be adjusted to change the event rate since the discriminator levels will no longer be correct. The rate can be modified with the dwell time as before and also by changing the distance between the Cs-137 source and scintillator. If the voltage/gain must be changed to get an acceptable event rate, the discriminator will also have to be reset in the PHA mode. Make 3 data runs as before to attain 3 different average event rates in each interval: i) 1–2 counts, ii) 5 counts, and iii) 10 counts. Save data to disk as a tab or comma delineated file.

==Analysis==
Using software of your choice, plot a histogram for each of your 6 data sets. Make sure the x-axis bins are configured for integer counts. For sufficiently low event rates, the
plotted distribution should be asymmetric and skewed towards the origin, consistent with Poisson statistics. There are statistical fluctuations associated with this measurement. These are distinguished from fluctuations due to instrumental uncertainty, for example, variation of the MCA measurement intervals. The statistical error can be obtained by doing this measurement repeatedly, but it is much easier to realize that the count in each histogram bin originates from random events. If Ck is the count in the kth bin, the uncertainty can be represented by the standard deviation σk associated with Poisson statistics: σk = √Ck. This is an important feature of Poisson statistics compared to a Gaussian distribution. In the latter, the standard deviation must be determined independently. Add statistical error bars σk to each point of
your histogram.

== Background Reading ==

[https://www.umass.edu/wsp/archive/reference/poisson/index.html The Poisson Distribution]

== History ==

Experiment set up and verified by Martin Hoeferkamp, January 2020

Poisson Statistics

2020-02-03T22:08:37Z

Somanakuttan: /* Equipment and Setup. */

Poisson Statistics

2020-02-03T22:03:13Z

Somanakuttan:

Poisson Statistics

2020-02-03T21:24:46Z

Somanakuttan: /* Background */

Poisson Statistics

2020-02-03T21:19:02Z

Somanakuttan:

== Background ==

[http://www.unm.edu/~mph/307/Poisson_UNM2.pdf Experiment Instructions (pdf)]

== Background Reading ==

[https://www.umass.edu/wsp/archive/reference/poisson/index.html The Poisson Distribution]

== History ==

Experiment set up and verified by Martin Hoeferkamp, January 2020

Computer Resources

2020-01-27T23:29:49Z

Somanakuttan: Created page with "{| class="wikitable" ! scope="col" style="width: 100px;" | Number on the Computer ! scope="col" style="width: 250px;" | RAM ! scope="col" style="width: 250px;" | Harddisk ! sc..."

{| class="wikitable"
! scope="col" style="width: 100px;" | Number on the Computer
! scope="col" style="width: 250px;" | RAM
! scope="col" style="width: 250px;" | Harddisk
! scope="col" style="width: 250px;" | Os installed
! scope="col" style="width: 250px;" | Processor
|-
| 18 || 2.0 GB || 75.0 GB || xUbuntu||Intel Core 2 Duo
|-
| 20 || 2.0 GB || 75.0 GB || windows 7.0||Intel Core 2 Duo
|-
| 22 || 2.0 GB || 75.0 GB || windows 7.0||Intel Core 2 Duo
|-
| 25 || 2.0 GB || 75.0 GB || windows 7.0||Intel Core 2 Duo
|-
|26 || 2.0 GB || 75.0 GB || windows 7.0||Intel Core 2 Duo
|-
|27 || 2.0 GB || 75.0 GB || windows 7.0||Intel Core 2 Duo
|-
|30 || 2.0 GB || 75.0 GB || windows 7.0||Intel Core 2 Duo
|-
|31 || 2.0 GB || 75.0 GB || windows 7.0||Intel Core 2 Duo
|-
|Dell Intel i5 || 8.0 GB || 930.0 GB || windows 10.0||Intel Core 5
|-