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- 7. One of the many isotopes used in cancer treatment is 198 Au, with a half-life of 2.70 d. Determine the mass of this isotope that is required to give an activity of 225 Ci. mg VJSS f60 ssf ( sf60 ssfE c) For a radio-nuclide, a number No of atoms at time t = 0 decays as N(t) = No e¯‹, where A is the decay constant. i) Derive the relationship between the half-life t₁ and the time constant □ = = 1/λ. 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 (\a << 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.The uranium isotope 238^U undergoes spontaneous alpha decay, becoming 234^Th. Calculate the recoil speed of the Th nuclei. a) 2.4x10^5 m/s b)1.5x10^5 m/s c)4.7x10^6 m/s d)1.0x10^3 m/s e)2.0x10^6 m/s
- The nuclide 198 Au, with a half-life of 2.70 d, is used in cancer therapy. What mass of this nuclide is required to provide an activity of 263 Ci? Number UnitsView imageTime 0 t₁2 20₁2 3₁/12 Number of nuclides, N x 10³ 1000 750 500 90/2 10/₁2 250 125 0 12 212 312 412 512 612 7h2 8h2 9h12 10/2 Time in multiples of t₁/2 The figure shows a typical radioactive decay (amount of undecayed nucleus (N) vs. time (t)) from a heavy nucleus. Such a decay may be best expressed by an equation like : ON = N₂ (xt) ON=N₂/λt -λt ON = N₂e N = N₂ e-1/At N 1,000,000 500,000 250,000 125,000 62,500 31,250 15,625 7,813 3,906 1,953 977 412 5/₁/2 61₁2 7h2 81/2
- A certain stable nuclide, after absorbing a neutron, emits an electron, and the new nuclide splits spontaneously into two alpha particles. Identify the nuclide.What is the half -life of potassium-40 if 1.70×10^19 nuclei have an activity of 300 BqIf 88 (atomic number) 228 (atomic mass) ?? is produced, determine the parent isotope for each of the following types of decay and justify your answer. a) alpha decay b) beta negative decay c) beta positive decay
- 11. Radium-226, 226Ra, undergoes an alpha decay. The current sample of Radium-226 has an initial activity of 5.50 × 101º Bq. (a) Identify the daughter nucleus by name, nucleon number, atomic number and neutron number. (b) What is the decay constant? (c) How many radioactive nuclei were initially present in the sample? (d) How long will it take the sample to reach an activity of 5.00 x 1010 Bq?Uranium-235 decays spontaneously by nucleon emission. a) Write a balanced equation to show the decay of Uranium-235, 2U, that leads to the formation of Uranium- 235 234 and name all the particles involved b) Write a balanced equation to show the decay of Uranium-235, U, that leads to the formation of 92 Thorium-231. Name all the particles involved.