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# 1 - positron silicon-28 mass number 28 28 atomic number 15...

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The symbol for phosphorus-28 = . The atomic weight of phosphorus is 31.0 . The atomic mass of phosphorus- 28 is about 28 . Therefore the nuclide is light compared to the stable isotopes of phosphorus . This means that the isotope has too few neutrons, or that its neutron/proton ratio is too low . It will decay to increase this ratio. This can be accomplished by either electron capture or positron emission, in which the mass number remains constant while the atomic number decreases. The nuclide with the same mass number but with an atomic number of 15 - 1 = 14 is silicon-28 = . Lighter atoms are more likely to decay by positron emission than by electron capture. In this case the decay is by positron emission. The reaction is: + Check: For both mass and charge to be conserved in a nuclear reaction: (1) The sum of the mass numbers for the products must equal the sum of the mass numbers for the reactants. (2) The sum of the atomic numbers for the products must equal the sum of the atomic numbers for the reactants. phosphorus-28

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Unformatted text preview: positron + silicon-28 + mass number: 28 + 28 atomic number: 15 1 + 14 Since radioactive decay is first order, the integrated rate law for a radioactive decay reaction is given by ln(N/N o ) = -kt where N o is the original number of radioactive nuclides, N is the number that remain at time t, and k is the rate constant for the reaction. The relation between the rate constant and the half-life for a first order reaction is kt 1/2 = ln 2 = 0.693 (1) Calculate the rate constant from the half-life given: half-life = t 1/2 = 27.7 days k = (ln 2 / t 1/2 ) = (0.693 / 27.7 days ) = 2.502E-2 d-1 (2) Calculate the time required for the activity to fall to 8.87 percent of its original value: The activity is directly proportional to the number or radioactive nuclides, N. Let N o be the original number of nuclides. N = 8.87E-2 x N o , where 8.87E-2 = 8.87 / 100 Then N/N o = 8.87E-2 Rearranging ln(N/N o ) = -kt t = -(1/k) x ln(N/N o ) = -(1 / 2.502E-2d-1 ) x ln ( 8.87E-2 ) = 96.8 d...
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