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Unformatted text preview: NUCLEAR PHYSICS E XERCISES Section 38.1 Elements, Isotopes, and Nuclear Structure 13. I NTERPRET This problem is about writing the conventional symbols for the isotopes of radon. D EVELOP The conventional symbol for a nucleus X is X, A Z where A is the mass number and Z is the atomic number. E VALUATE With the number of protons ( 86 Z = for all radon isotopes) and neutrons ( ) N A Z =- given, the mass numbers of the three isotopes are, respectively, 86 125 211, 220, A Z N = + = + = and 222. Therefore, the nuclear symbols are 211 220 222 86 86 86 Ra, Ra, and Ra. A SSESS Isotopes of a given element have the same number of protons (and hence Z ) but different number of neutrons (and hence A ). 14. 32 Z = for germanium (a semiconductor under silicon in the periodic table) so this isotope has A Z N = + = 32 44 76. + = Its symbol is 76 32 Ge. 15. I NTERPRET This problem asks for a comparison of the number of nucleons and charges between two nuclei. D EVELOP The comparison can be made by noting that the conventional symbol for a nucleus X is X, A Z where A is the mass number and Z is the atomic number. E VALUATE (a) The mass number (number of nucleons) is 35 A = for both. (b) The charge, , Ze of a potassium nucleus, 19, Z = is two electronic charge units greater than that for a chlorine nucleus, 17. Z = A SSESS 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, is 1.2 fm, while 52.9 pm a = is about 4 4.4 10 times larger. 17. I NTERPRET This problem is about the size of the fission products of 235 92 U. D EVELOP The nuclear radius can be estimated using Equation 38.1: 1/3 1/3 (1.2 fm) R R A A = = E VALUATE Two fission products as equal as possible would have 117 A = or 118, and radii of about 1/3 (1.2 fm) 5.9 fm. R A = A SSESS 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. I NTERPRET We determine the number of half-lives until a radioactive sample decays to 10% of its initial activity. This is a radioactive decay problem. D EVELOP We will use t N N e - = with 0.10 N N = and 1/ 2 ln 2 , t = and solve for t in terms of 1/ 2 . t E VALUATE 1/ 2 1/ 2 ln(0.10) 0.10 ln(0.10) 3.32 ln(2) t N N N e t t t t t - = = = - = - = 38.1 38 38.2 Chapter 38 A SSESS Lets see if that makes sense: after one half-life the activity is 1 2 the initial activity, after 2 its 1 4 , and after 3 its 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....
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