Chapter 29 - CHAPTER 29 Quick Quizzes 1. (c). At the end of...

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C HAPTER 29 Quick Quizzes 1. (c). At the end of the first half-life interval, half of the original sample has decayed and half remains. During the second half-life interval, half of the remaining portion of the sample decays. The total fraction of the sample that has decayed during the two half-lives is 111 3 222 4 ⎛⎞ += ⎜⎟ ⎝⎠ . 2. (b). If the original activity is , the activity remaining after an elapsed time t is 0 R ( ) 12 0.693 00 Tt t RR e R e λ == . Solving for the half-life yields () 0 ln = 0 0.96 = . If at 2.0 hr t = , the half-life is 2.0 h3 4 h l n0.96 T ⎡⎤ ⎢⎥ ⎣⎦ . 3. (a). Conservation of momentum requires the momenta of the two fragments be equal in magnitude and oppositely directed. Thus, from 2 2 KE p m = , the lighter alpha particle has more kinetic energy that the more massive daughter nucleus. 4. (a) and (b). Reactions (a) and (b) both conserve total charge and total mass number as required. Reaction (c) violates conservation of mass number with the sum of the mass numbers being 240 before reaction and being only 223 after reaction. 5. (b). In an endothermic reaction, the threshold energy exceeds the magnitude of the Q value by a factor of ( ) 1 mM + , where m is the mass of the incident particle and M is the mass of the target nucleus. 413
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CHAPTER 29 Problem Solutions 29.1 The average nuclear radii are 13 0 rr A = , where and A is the mass number. For 2 1 , 15 0 1. 21 0 m1 . 2 fm r = H ( )( ) 1.2 f m2 r == 1.5 fm For 60 , 27 Co ( )( ) m6 0 r 4.7 fm For 197 79 , Au ( )( ) 1.2 fm r 7.0 fm For 239 94 , Pu ( )( ) r 7.4 fm 29.2 An iron nucleus (in hemoglobin) has a few more neutrons than protons, but in a typical water molecule there are eight neutrons and ten protons. So protons and neutrons are nearly equally numerous in your body, each contributing (say) 35 kg out of a total body mass of 70 kg. -27 1 nucleon 35 kg 1.67 10 kg N ⎛⎞ = ⎜⎟ × ⎝⎠ 28 ~10 protons and ~10 neutron s The electron number is precisely equal to the proton number, e N = ~10 electron s 29.3 From 3 4 3 En n MV r ρρ π , we find ( ) ( ) 24 17 3 35.98 3 4 42 . 31 k gm E n M r πρ ⎡⎤ × = 2 81 0 m × ⎢⎥ × ⎣⎦ 29.4 The mass of the hydrogen atom is approximately equal to that of the proton, . If the radius of the atom is , then × 0.53 m r () ( ) ( ) 33 3 3 31.67 2. 71 k 43 40 . 53 m a mm Vr ρ × = = × × 414
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CHAPTER 29 The ratio of the nuclear density to this atomic density is 17 3 33 2. 31 0 k gm 71 k n a ρ × == × 13 8. 61 0 × 29.5 (a) ( ) () ()( ) ( ) 2 92 2 1 9 12 2 2 14 8.99 10 N m C 2 6 1.60 10 C 1.00 m e max min kqq F r ×⋅ × = 27.6 N × (b) -27 6.64 kg F a m α = × 27 2 4.16 m s × (c) ( ) 27.6 N1 . 00 m e min min PE F r r = × 1 MeV 2.76 J 1.60 J ⎛⎞ = 1.73 ⎜⎟ ⎝⎠ × 29.6 (a) From conservation of energy, KE PE =−∆ , or ( 2 1 2 mv q V ) = . Also, the centripetal acceleration is supplied by the magnetic force, so 2 qvB r = , or vq B r m = The energy equation then yields 2 2 rm V q B =∆ For , And C =12u m ( ) ( ) 2 19 2121.66 1000 V C0 .
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This homework help was uploaded on 03/21/2008 for the course PY 211 / 212 taught by Professor Chilton during the Spring '08 term at N.C. State.

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Chapter 29 - CHAPTER 29 Quick Quizzes 1. (c). At the end of...

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