 ## 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?

### 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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