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Revision as of 04:20, 21 February 2008

Alpha Particle Energy Loss

Barrett Nibling, Adolfo Gomez, Micheal Bouchey

February 20, 2008

Abstract

abstract here

List of Figures

figure 1

figure 2

figures 3

Introduction

intro here

Theory

Surface-Barrier Detectors

In this lab we are using an R-016-050-100 surface-barrier detector to measure the energy loss of alpha particles. The ORTEC model number mentioned above reflects three different parameters that are used to define a silicon surface-barrier detector. These parameters are resolution, active area, and depletion depth. In our model, the resolution is 16keV FWHM for 241-Am alphas, which comes from the 016. The active area is 50mm2, which comes from the 050. The depletion depth is 100µm, which comes from the 100.

Because the shape of the detector is a circular disk, the active area is the circular area of the face of the detector. At any distance from the source, a larger area means a larger angle and that means that more of the alpha particles emanating from the source will run in to the detector. This also implies that distance between the alpha source and the detector will affect the number of alpha particles that run in to the detector as well if the area is being held constant.

The depletion depth is the sensitive depth of the detector. The depth is important because it must be sufficient to completely stop all of the charged particles that are to be measured in the experiment. A 5.5MeV alpha particle is completely stopped with about 27µm of silicon. This means that, because natural alphas are usually less then 8MeV in energy, the 50µm detector used in this lab should stop all natural alphas.

Surface-barrier detectors are essentially 100% efficient for their active areas. This means that one can calculate the activity in alphas per second fairly easily

$Activity = (\frac{\Sigma_{\alpha}}{t}) (\frac{4 \pi s^2}{\pi r^2})$

Where

s = distance from source to detector

r = radius of the detector (cm)

t = time in seconds

Σα = counts in spectrum

1µCi = 3.7*104 disintegrations per second

Alpha Sources

In doing the experiment we see one peak for the Cm source. In reality a Cm source should show two peaks. This is because Cm is a very strong alpha source and so there is a thin metal foil over the Cm source for protection. The alpha particles loose energy in this foil which mean we cannot get an accurate base measurement from the Cm source. This is why there are two sources being used. The Po source is far less radioactive but is also unprotected and so it is used to gather our base reading.

The Cm source itself has a half-life of 18.1 years as opposed to the half-life of Po which is only 138 days. At 100% branching the Cm source has a Q-value of 5901.65 while the Po source has a Q-value of 5407.46. So the Cm source also has a much higher Q-value.

Procedure

procedure here

Example Image:

Schematic of Spectroscopy Apparatus

Results

Data here

Results 1

Example Table

The First Order Spectrum:

Helium, d=1/600mm, m=1
Color	$θ d i f f$ (degrees)	$λ$ (nm)	Error (nm)	Published $λ$ (nm)
Purple	15.6	448.0	$\pm$ 2.0	447.148
Teal	16.4	470.3	$\pm$ 2.0	471.314
Green	17.2	492.6	$\pm$ 2.0	492.193
Green	17.5	500.9	$\pm$ 2.0	501.567
Yellow//Orange	20.7	588.8	$\pm$ 2.0	587.562
Red	23.6	666.9	$\pm$ 2.0	667.815
Dim Red	25.1	706.7	$\pm$ 1.9	???

Results 2

Error Analysis

For the error analysis, there are two variable associated with an error, $θ d$ and $θ i$ .

The partial errors for each of the variable are calculated from the formulas

$\frac{\delta \lambda}{\delta \theta_{d}}=\frac{d}{m}Cos(\theta_{d})Sin({\delta \theta_{d}}),$

and,

$\frac{\delta \lambda}{\delta \theta_{i}}=\frac{d}{m}Cos(\theta_{i}) Sin({\delta \theta_{i}}).$

Then the total error is the sum of the two partial derivatives added in quadrature,

$\delta \lambda=\frac{d}{m} \sqrt{(\frac{\delta \lambda}{\delta \theta_{i}})^{2}+(\frac{\delta \lambda}{\delta \theta_{d}})^{2}}.$

The values for $δθ d$ and $δθ i$ used are half the value of the smallest unit of measure on the device, .05 degrees.

Conclusion

conclusion here

References

[1]

[2]

@@ Line 25: / Line 25: @@
 == Theory ==
-Theory here
+Surface-Barrier Detectors
-Example Math:
+In this lab we are using an R-016-050-100 surface-barrier detector to measure the energy loss of alpha particles.  The ORTEC model number mentioned above reflects three different parameters that are used to define a silicon surface-barrier detector.  These parameters are resolution, active area, and depletion depth.  In our model, the resolution is 16keV FWHM for 241-Am alphas, which comes from the 016.  The active area is 50mm2, which comes from the 050.  The depletion depth is 100µm, which comes from the 100.
-<center>
-<math>
-  Sin(\theta_{inc})+ Sin(\theta_{diff})=\frac{m \lambda}{d}
-</math>,
-</center>
-<center>
+Because the shape of the detector is a circular disk, the active area is the circular area of the face of the detector.  At any distance from the source, a larger area means a larger angle and that means that more of the alpha particles emanating from the source will run in to the detector.  This also implies that distance between the alpha source and the detector will affect the number of alpha particles that run in to the detector as well if the area is being held constant.
-<math>
-  Sin(\theta_{diff})=\frac{m \lambda}{d}.
-</math>
+The depletion depth is the sensitive depth of the detector.  The depth is important because it must be sufficient to completely stop all of the charged particles that are to be measured in the experiment.  A 5.5MeV alpha particle is completely stopped with about 27µm of silicon.  This means that, because natural alphas are usually less then 8MeV in energy, the 50µm detector used in this lab should stop all natural alphas.
-</center>
+Surface-barrier detectors are essentially 100% efficient for their active areas.  This means that one can calculate the activity in alphas per second fairly easily
 <center>
 <math>
-\lambda = \frac{d Sin(\theta_{diff})}{m}.
+Activity = (\frac{\Sigma_{\alpha}}{t}) (\frac{4 \pi s^2}{\pi r^2})
 </math>
 </center>
+Where
+s = distance from source to detector
+r = radius of the detector (cm)
+t = time in seconds
+Σα = counts in spectrum
+µCi = 3.7*104 disintegrations per second
+Alpha Sources
+In doing the experiment we see one peak for the Cm source.  In reality a Cm source should show two peaks.  This is because Cm is a very strong alpha source and so there is a thin metal foil over the Cm source for protection.  The alpha particles loose energy in this foil which mean we cannot get an accurate base measurement from the Cm source.  This is why there are two sources being used.  The Po source is far less radioactive but is also unprotected and so it is used to gather our base reading.
+The Cm source itself has a half-life of 18.1 years as opposed to the half-life of Po which is only 138 days.  At 100% branching the Cm source has a Q-value of 5901.65 while the Po source has a Q-value of 5407.46.  So the Cm source also has a much higher Q-value.
 == Procedure ==

Badboys/alpha

Revision as of 04:20, 21 February 2008

Contents

Abstract

List of Figures

Introduction

Theory

Procedure

Results

Results 1

Results 2

Error Analysis

Conclusion

References

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