### Relativistic Electron Lab

```Relativistic Electron Lab
• In this lab you will measure both the
momentum and kinetic energy of electrons
emitted from a radioactive source (b particles)
• The basic idea is to see that these quantities
require the use of relativistic equations and
that classical equations do not work since the
maximum b energy is 766 keV
• You will also measure the rest mass of the
electron and the speed of light in the lab.
Relativistic momentum
Remember this is a relativistic problem:
F = evB = γma (since F is perpendicular to v; otherwise it’s more complex);
but a = v2/r so that
evB = γmv2/r ; solving for r, we have
r = γmv/eB = p/eB so that we have p = eBr
Experiment Overview
• First you’ll calibrate the multichannel analyzer so
that we have a correspondence between channel
number and detected particle energy
• Second you’ll measure the
fixed radius of the orbit and
the slit widths (so you’ll
• Third, you’ll set and measure
B (fixing p), and then count
all detected particles that
have a corresponding kinetic
energy
Further Details - 1
• Chamber is evacuated using a mechanical pump
• B is measured using a Hall probe – must be oriented
properly to read B field in chamber (Hall probe)
• Source is a 10 mCi 204Tl beta emitter
• Detector is silicon surface-barrier detector – a stopped
charge particle produce ionization whose total charge is
proportional to the energy of the particle – this charge is
collected at an electrode (due to a 550 V potential applied
across it). The current pulse is then integrated by a preamp to produce a voltage pulse with an amplitude
proportional to the particle energy – this is amplified by a
linear amplifier and analyzed by a MCA to perform a PHA.
• The duration of the experiments should depend on B, with
longer experiments needed as B increases (range 5 to 12
hours)
Relativistic energy
Relativistic kinetic energy is given by:
 pc 
K  E  mc 
2
2
 mc
2

2
 mc
2
Manipulating this equation, we find:
 K  mc 
2
Or:
K  2mc
Solving for p2:
2
2
2
  pc    m c
K   mc
p
2
2
2K



2
2
2
2
  pc    m c
2
K
2c
2
m
2

2
Data Analysis
• You will, for each B, measure the kinetic
energy of the detected electrons
• Then from our derived equation connecting K
and p: p 2
K

2K
2c
2
m
You can plot this as y = (1/c2)x + m to find
values for c and m for the electron and to see
that the relativistic equations are correct vs
the classical K = p2/2m
Further Details – 2
• For each B, determine p with its uncertainty
• For each spectrum, determine the centroid of
the relativistic electron peak (in keV), its fullwidth-at-half-maximum (FWHM, also in keV),
and the net area (number of electrons) in the
peak
• In your graph, also plot classical and
relativistic theory and error bars on the points
This is a Collaborative Lab
• We will, all together, calibrate the MCA, you will
measure the geometry of the chamber; then we’ll
set-up and start the first run
• You will each take data on a schedule –
• You will need to:
–
–
–
–
–
Stop and save the experiment (in .SPC format)
Analyze the peak and record values
Re-measure the B field, after zeroing, and record
Re-set the B field, measure and record new value
Clear data and re-start experiment
Schedule
• Tuesday –
group: calibrate, measure and start B = 500 G
#1: ~6 h later – start B = 600 G
#2: Wed. AM – start 700 G
#3: late PM – start 800 G
#4: early Thurs AM – start 900 G
#5: Thurs evening – start 1000 G
#6: Friday AM – end and initial plot data; decide if
more needed (consult with me) and start new run or
close down
Room Key – outer and inner door keys hidden outside
N008
```