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Relativistic Electron Lab. In this lab you will measure both the momentum and kinetic energy of electrons emitted from a radioactive source ( b particles)

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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

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
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 know the spread in r)
  • Third, you’ll set and measure B (fixing p), and then count all detected particles that have a corresponding kinetic energy
further details 1
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 mCi204Tl 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 pre-amp 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 energy

Relativistic kinetic energy is given by:

Manipulating this equation, we find:

Or:

Solving for p2:

data analysis
Data Analysis
  • You will, for each B, measure the kinetic energy of the detected electrons
  • Then from our derived equation connecting K and p:

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
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 full-width-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
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
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