ch38-p069 - 69. (a) The transmission coefficient T for a...

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69. (a) The transmission coefficient T for a particle of mass m and energy E that is incident on a barrier of height U b and width L is given by 2 , bL Te = where () 2 2 8 . b mU E b h π− = For the proton, we have ( ) 22 7 1 3 2 34 14 1 8 1.6726 10 kg 10MeV 3.0MeV 1.6022 10 J MeV 6.6261 10 J s 5.8082 10 m . b −− π× × = ×⋅ This gives ( ) 14 1 15 5.8082 10 m 10 10 m 5.8082, bL × = and 2(5.8082) 6 9.02 10 . == × The value of b was computed to a greater number of significant digits than usual because an exponential is quite sensitive to the value of the exponent. (b) Mechanical energy is conserved. Before the proton reaches the barrier, it has a kinetic energy of 3.0 MeV and a potential energy of zero. After passing through the barrier, the proton again has a potential energy of zero, thus a kinetic energy of 3.0 MeV. (c) Energy is also conserved for the reflection process. After reflection, the proton has a potential energy of zero, and thus a kinetic energy of 3.0 MeV.
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This note was uploaded on 06/03/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.

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ch38-p069 - 69. (a) The transmission coefficient T for a...

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