# Irodov Solutions → Atomic and Nuclear Physics → Radioactivity

 6.214. Knowing the decay constant λ of a nucleus, find: (a) the probability of decay of the nucleus during the time from 0 to t; (b) the mean lifetime τ of the nucleus. Free solution >> 6.215. What fraction of the radioactive cobalt nuclei whose half-life is 71.3 days decays during a month? Free solution >> 6.216. How many beta-particles are emitted during one hour by 1.0 μg of Na24 radionuclide whose half-life is 15 hours? Free solution >> 6.217. To investigate the beta-decay of Mg23 radionuclide, a counter was activated at the moment t = 0. It registered N1 beta-particles by a moment t1 = 2.0 s, and by a moment t2 = 3t1 the number of registered beta-particles was 2.66 times greater. Find the mean lifetime of the given nuclei. Free solution >> 6.218. The activity of a certain preparation decreases 2.5 times after 7.0 days. Find its half-life. Free solution >> 6.220. Find the decay constant and the mean lifetime of Co55 radionuclide if its activity is known to decrease 4.0% per hour. The decay product is nonradioactive. Free solution >> 6.221. A U238 preparation of mass 1.0 g emits 1.24*104 alpha-particles per second. Find the half-life of this nuclide and the activity of the preparation. Free solution >> 6.222. Determine the age of ancient wooden items if it is known that the specific activity of C14 nuclide in them amounts to 3/5 of that in lately felled trees. The half-life of C14 nuclei is 5570 years. Free solution >> 6.223. In a uranium ore the ratio of U238 nuclei to Pb206 nuclei is η = 2.8. Evaluate the age of the ore, assuming all the lead Pb206 to be a final decay product of the uranium series. The half-life of U238 nuclei is 4.5*109 years. Free solution >> 6.225. A small amount of solution containing Na24 radionuclide with activity A = 2.0*103 disintegrations per second was injected in the bloodstream of a man. The activity of 1 cm3 of blood sample taken t = 5.0 hours later turned out to be A' = 16 disintegrations per minute per cm3. The half-life of the radionuclide is T = 15 hours. Find the volume of the man's blood. Free solution >> 6.229. A radionuclide A1 with decay constant λ1 transforms into a radionuclide A2 with decay constant λ2. Assuming that at the initial moment the preparation contained only the radionuclide A1, find: (a) the equation describing accumulation of the radionuclide A2 with time; (b) the time interval after which the activity of radionuclide A2 reaches the maximum value. Free solution >> 6.231. A radionuclide A1 goes through the transformation chain A1 → A2 → A3 (stable) with respective decay constants λ1 and λ2. Assuming that at the initial moment the preparation contained only the radionuclide A1 equal in quantity to N10 nuclei, find the equation describing accumulation of the stable isotope A3. Free solution >> 6.234. A stationary Pb200 nucleus emits an alpha-particle with kinetic energy Tα = 5.77 MeV. Find the recoil velocity of a daughter nucleus. What fraction of the total energy liberated in this decay is accounted for by the recoil energy of the daughter nucleus? Free solution >> 6.236. The alpha-decay of Po210 nuclei (in the ground state) is accompanied by emission of two groups of alpha-particles with kinetic energies 5.30 and 4.50 MeV. Following the emission of these particles the daughter nuclei are found in the ground and excited states. Find the energy of gamma-quanta emitted by the excited nuclei. Free solution >> 6.241. Taking the values of atomic masses from the tables, calculate the kinetic energies of a positron and a neutrino emitted by C11 nucleus for the case when the daughter nucleus does not recoil. Free solution >> 6.242. Find the kinetic energy of the recoil nucleus in the positronic decay of a N13 nucleus for the case when the energy of positrons is maximum. Free solution >> 6.243. From the tables of atomic masses determine the velocity of a nucleus appearing as a result of K-capture in a Be7 atom provided the daughter nucleus turns out to be in the ground state. Free solution >> 6.244. Passing down to the ground state, excited Ag109 nuclei emit either gamma quanta with energy 87 keV or K conversion electrons whose binding energy is 26 keV. Find the velocity of these electrons. Free solution >> 6.245. A free stationary Ir191 nucleus with excitation energy E = 129 keV passes to the ground state, emitting a gamma quantum. Calculate the fractional change of gamma quanta energy due to recoil of the nucleus. Free solution >> 6.246. What must be the relative velocity of a source and an absorber consisting of free Ir191 nuclei to observe the maximum absorption of gamma quanta with energy ε = 129 keV? Free solution >> 6.247. A source of gamma quanta is placed at a height h = 20 m above an absorber. With what velocity should the source be displaced upward to counterbalance completely the gravitational variation of gamma quanta energy due to the Earth's gravity at the point where the absorber is located? Free solution >> 6.248. What is the minimum height to which a gamma quanta source containing excited Zn67 nuclei has to be raised for the gravitational displacement of the Mossbauer line to exceed the line width itself, when registered on the Earth's surface? The registered gamma quanta are known to have an energy ε = 93 keV and appear on transition of Zn67 nuclei to the ground state, and the mean lifetime of the excited state is τ = 14 μs. Free solution >>