p39_079

p39_079 - 79(a The transmission coecient T for a particle...

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79. (a) The transmission coeﬃcient T for a particle of mass m and energy E that is incident on a barrier of height U and width L is given by T = e 2 kL , where k = r 8 π 2 m ( U E ) h 2 . For the proton, k = s 8 π 2 (1 . 6726 × 10 27 kg)(10 MeV 3 . 0 MeV)(1 . 6022 × 10 13 J / MeV) (6 . 6261 × 10 34 J · s) 2 =5 . 8082 × 10 14 m 1 , kL =(5 . 8082 × 10 14 m 1 )(10 × 10 15 m) = 5 . 8082, and T = e 2 × 5 . 8082 =9 . 02 × 10 6 . The value of k was computed to a greater number of signi±cant digits than usual because an exponential is quite sensitive to the value of the exponent. The mass of a deuteron is 2 . 0141 u = 3 . 3454 × 10 27 kg, so k = s 8 π 2 (3 . 3454 × 10 27 kg)(10 MeV 3 . 0 MeV)(1 . 6022 × 10 13 J / MeV) (6 . 6261 × 10 34 J · s) 2 =8 . 2143 × 10 14 m 1 , =(8 . 2143 × 10 14 m 1 )(10 × 10
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.

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