Irodov Solutions → Atomic and Nuclear Physics → Radioactivity 
6.214. Knowing the decay constant λ of a nucleus, find:
6.215. What fraction of the radioactive cobalt nuclei whose halflife is 71.3 days decays during a month?
6.216. How many betaparticles are emitted during one hour by 1.0 μg of Na^{24} radionuclide whose halflife is 15 hours?
6.217. To investigate the betadecay of Mg^{23} radionuclide, a counter was activated at the moment t = 0. It registered N_{1} betaparticles by a moment t_{1} = 2.0 s, and by a moment t_{2} = 3t_{1} the number of registered betaparticles was 2.66 times greater. Find the mean lifetime of the given nuclei.
6.218. The activity of a certain preparation decreases 2.5 times after 7.0 days. Find its halflife.
6.220. Find the decay constant and the mean lifetime of Co^{55} radionuclide if its activity is known to decrease 4.0% per hour. The decay product is nonradioactive.
6.221. A U^{238} preparation of mass 1.0 g emits 1.24*10^{4} alphaparticles per second. Find the halflife of this nuclide and the activity of the preparation.
6.222. Determine the age of ancient wooden items if it is known that the specific activity of C^{14} nuclide in them amounts to 3/5 of that in lately felled trees. The halflife of C^{14} nuclei is 5570 years.
6.223. In a uranium ore the ratio of U^{238} nuclei to Pb^{206} nuclei is η = 2.8. Evaluate the age of the ore, assuming all the lead Pb^{206} to be a final decay product of the uranium series. The halflife of U^{238} nuclei is 4.5*10^{9} years.
6.225. A small amount of solution containing Na^{24} radionuclide with activity A = 2.0*10^{3} disintegrations per second was injected in the bloodstream of a man. The activity of 1 cm^{3} of blood sample taken t = 5.0 hours later turned out to be A' = 16 disintegrations per minute per cm^{3}. The halflife of the radionuclide is T = 15 hours. Find the volume of the man's blood.
6.229. A radionuclide A_{1} with decay constant λ_{1} transforms into a radionuclide A_{2} with decay constant λ_{2}. Assuming that at the initial moment the preparation contained only the radionuclide A_{1}, find:
6.231. A radionuclide A_{1} goes through the transformation chain A_{1} → A_{2} → A_{3} (stable) with respective decay constants λ_{1} and λ_{2}. Assuming that at the initial moment the preparation contained only the radionuclide A_{1} equal in quantity to N_{10} nuclei, find the equation describing accumulation of the stable isotope A_{3}.
6.234. A stationary Pb^{200} nucleus emits an alphaparticle with kinetic energy T_{α} = 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?
6.236. The alphadecay of Po^{210} nuclei (in the ground state) is accompanied by emission of two groups of alphaparticles 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 gammaquanta emitted by the excited nuclei.
6.241. Taking the values of atomic masses from the tables, calculate the kinetic energies of a positron and a neutrino emitted by C^{11} nucleus for the case when the daughter nucleus does not recoil.
6.242. Find the kinetic energy of the recoil nucleus in the positronic decay of a N^{13} nucleus for the case when the energy of positrons is maximum.
6.243. From the tables of atomic masses determine the velocity of a nucleus appearing as a result of Kcapture in a Be^{7} atom provided the daughter nucleus turns out to be in the ground state.
6.244. Passing down to the ground state, excited Ag^{109} 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.
6.245. A free stationary Ir^{191} 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.
6.246. What must be the relative velocity of a source and an absorber consisting of free Ir^{191} nuclei to observe the maximum absorption of gamma quanta with energy ε = 129 keV?
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?
6.248. What is the minimum height to which a gamma quanta source containing excited Zn^{67} 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 Zn^{67} nuclei to the ground state, and the mean lifetime of the excited state is τ = 14 μs.
