The Velocity of Alpha Particles

Equipment

Stage, camera holder, source holder, polonium-210, Minipix-EDU

Procedure

1. Launch the Pixet Basic software and modify settings to the following:
   1. Min Level: 0
   2. Max Level: 100
   3. Measurement Mode: Tracking
   4. Frames: 100
   5. Exposure: 1 s
   6. Sum: uncheck
   7. Color Map: Hot
2. Mount the MiniPix EDU camera and the holder with polonium on the stage.
3. Keep the camera and the source as close as possible.
4. Start the scan and save the data.

Results

1. From the histogram (Fig. 1), we may observe the energy of alpha particles to be 4210 keV
   
   
   Figure 1. The histogram in the spectra section displays the energy of alpha particles from polonium-210
   
   
2. The relativistic energy of a particle is given by the following equation:
   
   E = E₀ + E_k
   
   where E₀ (3735000 keV for alpha particles) is rest energy and E_k is the kinetic energy. If we substitute  , we get the following equation:
   
   
   
3. Another method of calculating the velocity ratio is using the classical equation of kinetic energy:
   
   
   
   
4. Substituting the values in equation 2 and 3, (m = 6.64 x 10^-27 kg):
   
   
   

Conclusion

1. The velocity of alpha particles is 0.0473c or ~5% the speed of light.
2. The velocity of an alpha particle is relatively very less than that of light, thus we do not observe any difference in result from relative and classical equations. This might not be the case with beta particles as they travel almost 90% of the speed of light.
3.  Since the kinetic energy of an alpha particle is significantly smaller than its rest energy, the deviation of classical and relativistic v/c is very small.