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1. What is the ratio of cyclotron frequencies calculated relativistic ally and nonrelativistic ally for (a) a 12-MeV proton, (b) a 120-MeV proton, and (c) a 1.2-GeV proton?

2. A 33-GeV proton is said to take about half a second to make some 160,000 revolutions around the 0.80-km circumference of the Alternating Gradient Synchrotron at Brookhaven. Check this statement.

3. Science ?ction stories have included spaceships that use the annihilation of matter and antimatter to produce energy. How much matter and antimatter would be required to launch a 15,000-kg spaceship from Earth's orbit out of the solar system? Ignore the energy necessary to escape Earth's gravity, and assume equal amounts of matter and antimatter.

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