c) For a radio-nuclide, a number No of atoms at time t = 0 decays as N(t) = No ext, where \ is the decay constant. i) Derive the relationship between the half-life t₁ and the time constant 7 = 1/λ. 2 ii) The radio-nuclide radium-226 has a half-life of 1600 years. Calculate the activity of one gram of radium in Becquerels. iii) Radium-226 decays to radon-222, known as the daughter product. The amount of a daughter product present will vary with time, Na(t). Sketch two graphs, with appropri- ate axes and labels, to show schematically how N(t) and Na(t) evolve if Na(0) = 0, for the two extreme cases where the daughter product is much more radioactive than the parent (\d >> \) and where the daughter product is much less radioactive than the parent (\d << λ). Given that the half-life of radon-226 is 3.8 days, indicate which graph is relevant and estimate the amount of radon in equilibrium with one mole of radium.

c) For a radio-nuclide, a number No of atoms at time t = 0 decays as N(t) = No ext, where \ is the decay constant. i) Derive the relationship between the half-life t₁ and the time constant 7 = 1/λ. 2 ii) The radio-nuclide radium-226 has a half-life of 1600 years. Calculate the activity of one gram of radium in Becquerels. iii) Radium-226 decays to radon-222, known as the daughter product. The amount of a daughter product present will vary with time, Na(t). Sketch two graphs, with appropri- ate axes and labels, to show schematically how N(t) and Na(t) evolve if Na(0) = 0, for the two extreme cases where the daughter product is much more radioactive than the parent (\d >> \) and where the daughter product is much less radioactive than the parent (\d << λ). Given that the half-life of radon-226 is 3.8 days, indicate which graph is relevant and estimate the amount of radon in equilibrium with one mole of radium.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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