Chapter42

# Chapter42 - 42.1 Model The nucleus is composed of Z protons...

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42.1. Model: The nucleus is composed of Z protons and Α Ζ neutrons. Solve: (a) 3 H has Z = 1 proton and 3 1 = 2 neutrons. (b) 40 Ar has Z = 18 protons and 40 18 = 22 neutrons. (c) 40 Ca has Z = 20 protons and 40 20 = 20 neutrons. (d) 239 Pu has Z = 94 protons and 239 94 = 145 neutrons.

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42.2. Model: The nucleus is composed of Z protons and Α Ζ neutrons. Solve: (a) 3 He has Z = 2 protons and 3 2 = 1 neutrons. (b) 20 Ne has Z = 10 protons and 20 10 = 10 neutrons. (c) 60 Co has Z = 27 protons and 60 27 = 33 neutrons. (d) 226 Ra has Z = 88 protons and 226 88 = 138 neutrons.
42.3. Solve: (a) The radius and diameter of the nucleus of 4 He are r = r 0 A 1/3 = (1.2 fm)(4) 1/3 = 1.90 fm d = 3.8 fm (b) For 40 Ar, r = (1.2 fm)(40) 1/3 = 4.10 fm and d = 8.2 fm. (c) For 220 Rn, r = (1.2 fm)(220) 1/3 = 7.24 fm and d = 14.5 fm.

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42.4. Solve: Using Equation 42.2, r = r 0 A 1/3 8.84 fm = 2(1.2 fm) A 1/3 ⇒= = A 8.84 fm 2.4 fm 3 50 Both titanium and chromium have stable isotopes of A = 50.
42.5. Model: Assume that air is 21% O 2 and 79% N 2 , and that its density is 1.2 kg/m 3 . Solve: The masses of oxygen and nitrogen molecules are M oxygen = (0.21) ρ air V = (0.21)(1.2 kg/m 3 )(1 m 3 ) = 0.252 kg M nitrogen = (0.79) air V = 0.79(1.2 kg/m 3 )(1 m 3 ) = 0.948 kg The number of oxygen molecules is N M M N A A oxygen oxygen 0.252 kg 0.032 kg / mol mol == × ×= × 6 02 10 4 74 10 23 1 24 .. The number of protons from oxygen molecules is N oxygen protons × = × 4 743 10 16 7 59 10 24 25 Likewise, the number of protons from nitrogen molecules is N nitrogen protons 0.948 kg 0.028 kg / mol mol × × = × 6 02 10 14 2 85 10 23 1 26 The total number of protons is 7.59 × 10 25 + 2.85 × 10 26 = 3.6 × 10 26 . Because nitrogen and oxygen each have an equal number of protons and neutrons, this is also the total number of neutrons.

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42.6. Model: Assume that your body has a weight of 170 pounds or 77 kg. Also, assume that a human body is 100% water. Solve: The number of water molecules is N water 77 kg 0.018 kg / mol mol × = × 6 02 10 2 575 10 23 1 27 .. The total number of protons and neutrons are N protons = 2.575 × 10 27 × 10 = 2.6 × 10 28 N neutrons = 2.575 × 10 27 × 8 = 2.1 × 10 28 Assess: Your estimate will differ, depending on your mass, but should not differ by more than a factor of 2.
42.7. Solve: The nuclear density was found to be 2.3 × 10 17 kg / m 3 . Thus MV == × () × ρ π nuclear 3 kg / m m kg 23 10 4 3 05 10 12 10 17 2 3 11 .. . Assess: The nuclear density is tremendously large compared to the density of familiar liquids and solids.

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42.8. Solve: The chart shows stable and unstable nuclei for all nuclei with Z 8. A black dot represents stable isotopes, a dark gray dot represents isotopes that undergo beta-minus decay, and a light gray dot represents isotopes that undergo beta-plus decay or electron-capture decay.
42.9. Solve: (a) A = 36, for which 36 S and 36 Ar are stable. (b) Nuclei with A = 8 and A = 5 have no stable nuclei.

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42.10. Solve: From Equation 42.6, the binding energy for 3 H is BZ m N mm =+ () = + = H n atom 1.00783 u 1.00866 u 3.01605 u 0.00910 u 931.49 MeV / u 8.476 MeV 12 The binding energy per nucleon is 1 3 8.476 MeV 2.83 MeV = . For 3 He , the binding energy is m m =+− = + = H n atom 1.00783 u 1.00866 u 3.01603 u 0.00829 u 931.49 MeV / u 7.722 MeV 21 The binding energy per nucleon is 1 3 7.722 MeV 2.57 MeV = .
42.11.

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Chapter42 - 42.1 Model The nucleus is composed of Z protons...

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