Chapter38 - NUCLEAR PHYSICS 38 EXERCISES Section 38.1...

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38.1 NUCLEAR PHYSICS EXERCISES Section 38.1 Elements, Isotopes, and Nuclear Structure 13. INTERPRET This problem is about writing the conventional symbols for the isotopes of radon. DEVELOP The conventional symbol for a nucleus X is Z A X, where A is the mass number and Z is the atomic number. EVALUATE With the number of protons ( Z = 86 for all radon isotopes) and neutrons () NAZ =− given, the mass numbers of the three isotopes are, respectively, AZN =+= + = 86 125 211, 220, and 222. Therefore, the nuclear symbols are 86 211 86 220 86 222 Ra Ra, and Ra. , ASSESS Isotopes of a given element have the same number of protons (and hence Z ) but different number of neutrons (and hence A ). 14. Z = 32 for germanium (a semiconductor under silicon in the periodic table) so this isotope has =+= 32 44 76 += . Its symbol is 32 76 Ge. 15. INTERPRET This problem asks for a comparison of the number of nucleons and charges between two nuclei. DEVELOP The comparison can be made by noting that the conventional symbol for a nucleus X is Z A X, where A is the mass number and Z is the atomic number. EVALUATE (a) The mass number (number of nucleons) is A = 35 for both. (b) The charge, Ze , of a potassium nucleus, Z = 19, is two electronic charge units greater than that for a chlorine nucleus, Z = 17. ASSESS Equality in mass number A does not imply equality in atomic number Z . Two nuclei have the same Z only when they are isotopes. 16. The “radius” of the proton, implied by Equation 38.1, is12 .f m , while a 0 52 9 = .p m is about44 10 4 . × times larger. 17. INTERPRET This problem is about the size of the fission products of 92 235 U. DEVELOP The nuclear radius can be estimated using Equation 38.1: RR A A == 0 13 12 // (. ) fm EVALUATE Two fission products as equal as possible would have A = 117 or 118, and radii of about RA =≈ ) . 59 fm. / ASSESS Equation 38.1 is a good approximation for R since nucleons are packed tightly into the nucleus. The tight packing also suggests that all nuclei have roughly the same density. Section 38.2 Radioactivity 18. INTERPRET We determine the number of half-lives until a radioactive sample decays to 10% of its initial activity. This is a radioactive decay problem. DEVELOP We will use NN e t = 0 λ with = 010 0 . and = ln / , 2 t and solve for t in terms of t / . 38
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38.2 Chapter 38 EVALUATE NN N e t t t == = = 010 00 .l n ( . ) ln( . ) ln( λ 2 332 12 ) . // tt t →= ASSESS Let’s see if that makes sense: after one half-life the activity is 1 2 the initial activity, after 2 it’s 1 4 , and after 3 it’s 1 8 .10% is just a bit less than 1 8 , so our answer of a little more than three half-lives is about right. 19. INTERPRET In this problem we are asked to write down all possible beta-decay processes for 29 64 Cu. DEVELOP Beta decay in 29 64 Cu can involve positron-neutrino or electron-anti-neutrino emission, or electron capture. EVALUATE The reactions are: 29 64 29 64 40 Cu Zn Cu Ni 30 64 28 64 →+ + + + βν (% ) ) ) 19 41 29 64 Cu Ni 28 64 +→ + e ν ASSESS In each decay mode, charge and mass number are conserved.
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This note was uploaded on 10/21/2010 for the course PHYSICS 2131441 taught by Professor Pheong during the Fall '10 term at University of California, Berkeley.

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Chapter38 - NUCLEAR PHYSICS 38 EXERCISES Section 38.1...

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