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Assignment01

# Assignment01 - Duke University Medical Physics Program...

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Duke University Medical Physics Program MP200 - Radiation Physics Fall 2010 Assignment 01 Due 09/13/10 ( Show your work for each problem. Partial credits are awarded.) 1. Calculate the minimum coefficient of friction necessary to keep a thin circular ring from sliding as it rolls down a plane inclined at an angle θ with respect to the horizontal plane. 2. Find < x > and < x 2 > for the first excited state ( n = 2) in an infinite square-well potential. 3. An electron is in a box of length 0 . 1 nm . Find its minimum kinetic energy. 4. A particle has the wave function ψ ( r ) = Ne - αr Where N is a normalization factor and α is a known real parame- ter. (a) Calculate the factor N . (b) Calculate the expectation values < x > , < r > , < r 2 > in this state. (c) Calculate the uncertainties (Δ x ) 2 and (Δ r ) 2 . (d) Calculate the probability of finding the particle in the region r > Δ r 5. A particle of rest mass 1 MeV/c 2 and kinetic energy 4 MeV col- lides with a stationary particle of rest mass 3 MeV/c 2 . After the 1

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collision, the two particle stick together. Find (a) the initial mo- mentum of the system (b) the final velocity of the two-particle system, and (c) the rest mass of the two-particle system. 6. Two particles with the same mass m are emitted in the same di- rection, with momenta 10 mc and 20 mc respectively. As seen from the slower one what is the velocity of the faster particle, and vice verse? 7. A particle of rest energy 494 MeV decays into a μ meson of rest energy 106 MeV and a neutrino of zero rest energy. Find the ki- netic energies of the μ meson and neutrino into which the K meson decays while at rest. 8. How much energy is required to accelerate an electron from rest to a speed of 0 . 9 c ? 9. A meter stick is observed to be only 0 . 9 m long to an inertial ob- server. At what speed, relative to the observer, must the meter stick be moving? (a) 0 . 44 × 10 8 m/s (b)0 . 57 × 10 8 m/s (c)0 . 95 × 10 8 m/s (d)
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