HW10.pdf - MODERN PHYSICS 14-20 Ek =(a p2 mv 2 3 = = kB T...

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MODERN PHYSICS 231 14-20 = = = 2 2 B 3 2 2 2 k p mv E k T m where = × 23 B 1.38 10 J K k , = 300 K T , and = × 27 1.67 10 kg m . (a) ( ) ( ) ( ) ( ) ( ) = = × × 1 2 1 2 27 23 B 3 3 1.67 10 kg 1.38 10 J K 300 K p mk T = × 24 4.55 10 kg m s p (b) λ × = = × 34 24 6.63 10 J s 4.55 10 kg m s h p λ = × = 10 1.46 10 m 1.46 Å = 0.146 nm . This is about 5 10 times nuclear sizes and about the same size as atomic sizes. 14-21 ( ) = 2 U Ba Kr n E c m m m m ( ) ( ) [ ] ( ) [ ] = = = 931.5 MeV u 235.043 9 u 140.913 9 u 91.897 3 u 2 1.008 7 u 931.5 MeV u 0.215 3 u 200.6 MeV E E 14-22 (a) ( ) ( ) ( ) ( ) ( )( ) × × × = 24 9 13 1.66 10 g u 10 W 1day 24 h day 3 600 s h nucleon 200 MeV 235.04 u 1.6 10 J MeV 1 050 g (b) π ρ = 3 4 3 r m ; diameter ( ) π ρ π × × = = = = 1 3 1 3 3 3 6 1.05 10 g 6 2 4.759 cm 18.79 g cm m r 14-23 (a) For a sphere: π = 3 4 3 V r and ( ) π = 1 3 3 4 V r , so ( ) π π = = 2 1 3 3 4 4.84 4 3 r A V V r . (b) For a cube: = 3 V l and = 1 3 l V , so = = 2 1 3 3 6 6 A l V V l . (c) For a parallelepiped: = 3 2 V a and ( ) = 1 3 2 a V , so + = = 2 2 1 3 3 2 8 6.30 2 A a a V V a .
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