Units in Particle Physics: Practice Problems and Answers

Practice Problems

1. A proton in the Fermilab Tevatron has an energy of 1.00 TeV. What is this energy in Joules?
   
   
2. A 2.00 g bug moves at 0.100 cm/s. Find its momentum and kinetic energy in TeV.
   
   
3. The mass of a proton is 1.67 x 10^-27 kg. Convert this to GeV and TeV.
   
   
4. The mass of an electron is 0.511 MeV. Convert to kg.
   
   
5. The electron accelerator at Jefferson Lab in Virginia runs at a beam energy of about a 5.5 GeV. Because they have so little mass, we can say the momentum of any one of these electrons is also 5.5 GeV. What is that in kg-m/s?

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Solutions

1. 1.609 x 10^-7 J (see table)
   
   
2. p = mv = (2.00 x 10^-3 kg)(1.00 x 10^-3 m/s) = 2.00 x 10^-6 kg-m/s
   Then (2.00 x 10^-6 kg-m/s) / (5.36 x 10^-16 kg-m-c/s-TeV) = 3.73 x 10 ⁹ TeV/c
   
   K = 0.5mv² = 0.5(2.00 x 10^-3 kg)1.00 x 10^-3 m/s)² = 1.00 x 10^-9 J
   Then (1.00 x 10^-9 J) / (1.609 x 10^-7 J/TeV) = 6.22 x 10^-3 TeV
   
   
3. (1.67 x 10^-27 kg) / (1.79 x 10^-27 kg-c²/GeV) = 0.933 GeV/c²
   The quick way to get TeV is to divide by 1000: (0.933 GeV/c²) / (1000 TeV/GeV) = 9.33 x 10^-4 TeV/c²
   Note: The actual proton mass, calculated more precisely, is closer to 0.938 GeV/c².
   
   
4. (0.511 MeV/c²)(1.79 x10^-30 kg-c²/MeV) = 9.15 x 10^-31 kg
   
   
5. (5.5 GeV/c)(5.36 x 10^-19 kg-m-c/s-GeV) = 3.0 x 10^-18 kg-m/s
   
   

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