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Free 238U nuclei kept in a train emit alpha particles. When the train is stationary and a uranium nucleus decays, a passenger measures that the separation between the alpha particle and the recoiling nucleus becomes x in time t after the decay. If a decay takes place when the train is moving at a uniform speed v, the distance between the alpha particle and the recoiling nucleus at a time t after the decay, as measured by the passenger will be
During a nuclear fission reaction,
In the decay 64Cu → 64Ni + e+ + v, the maximum kinetic energy carried by the positron is found to be 0.650 MeV.
(a) What is the energy of the neutrino which was emitted together with a positron of kinetic energy 0.150 MeV?
(b) What is the momentum of this neutrino in kg ms–1? Use the formula applicable to a photon.
Carbon (Z = 6) with mass number 11 decays to boron (Z = 5).
(a) Is it is β+-decay or a β–-decay?
(b) The half-life of the decay scheme is 20.3 minutes. How much time will elapse before a mixture of 90% carbon-11 and 10% boron-11 (by the number of atoms) converts itself into a mixture of 10% carbon-11 and 90% boron-11?
A point source emitting alpha particles is placed at a distance of 1m from a counter which records any alpha particle falling on its 1 cm2 window. If the source contains 6.0 × 1016 active nuclei and the counter records a rate of 50000 counts/second, find the decay constant. Assume that the source emits alpha particles uniformly in all directions and the alpha particles fall nearly normally on the window.
238U decays to 206Pb with a half-life of 4.47 × 109 y. This happens in a number of steps. Can you justify a single half-life for this chain of processes? A sample of rock is found to contain 2.00 mg of 238U and 0.600 mg of 206Pb. Assuming that all the lead has come from uranium, find the life of the rock.
Natural water contains a small amount of tritium . This isotope beta-decays with a half-life of 12.5 years. A mountaineer while climbing towards a difficult peak finds debris of some earlier unsuccessful attempt. Among other things he finds a sealed bottle of whisky. On return 1.5 per cent of the radioactivity as compared to a recently purchased bottle marked ‘8 years old’. Estimate the time of that unsuccessful attempt.
decays to through electron capture with a decay constant of 0.257 per day.
(a) What other particle or particles are emitted in the decay?
(b) Assume that the electron is captured from the K shell. Use Mosley’s law √v = α (Z – b) with α = 4.95 × 107 s–1/2 and b = 1 to find the wavelength of the Kα X-ray emitted following the electron capture.
In an agricultural experiment, a solution containing 1 mole of a radioactive material (t1/2 = 14.3 days) was injected into the roots of a plant. The plant was allowed 70 hours to settle down and then activity was measured in its fruit. If the activity measured was 1 μCi, what per cent of activity is transmitted from the root to the fruit in steady state?
can disintegrate either by emitting an α-particle or by emitting a β–-particle.
(a) Write the two equations showing the products of the decays.
(b) The probabilities of disintegration by α-and β-decays are in the ratio 7/13. The overall half-life of 212Bi is one hour. If 1g of pure 212Bi is taken at 12.00 noon, what will be the composition of this sample at 1 p.m. the same day?
A sample contains a mixture of 110Ag and 108Ag isotopes each having an activity of 8.0 × 108 disintegrations per second. 108Ag is known to have larger half-life than 110Ag. The activity A is measured as a function of time and the following data are obtained.
(a) Plot ln(A/A0) versus time.
(b) See that for large values of time, the plot is nearly linear. Deduce the half-life of 108Ag from this portion of the plot.
(c) Use the half-life of 108Ag to calculate the activity corresponding to 110Ag in the first 50 s.
(d) Plot ln(A/A0) versus time for 110Ag for the first 50 s.
(e) Find the half-life of 108Ag.
A human body excretes (removes by waste discharge, sweating, etc.) certain materials by a law similar to radioactivity. If technetium is injected in some form in a human body, the body excretes half the amount in 24 hours. A patient is given an injection containing 99Tc. This isotope is radioactive with a half-life of 6 hours. The activity from the body just after the injection is 6 μCi. How much time will elapse before the activity falls to 3 μCi?
Radioactive isotopes are produced in a nuclear physics experiment at a constant rate dN/dt = R. An inductor of inductance 100 mH, a resistor of resistance 100 Ω and a battery are connected to form a series circuit. The circuit is switched on at the instant the production of radioactive isotope starts. It is found that i/N remains constant in time where i is the current in the circuit at time t and N is the number of active nuclei at time t. Find the half-life of the isotope.
A town has a population of 1 million. The average electric power needed per person is 300W. A reactor is to be designed to supply power to this town. The efficiency with which thermal power is converted into electric power is aimed at 25%.
(a) Assuming 200 MeV of thermal energy to come from each fission event on an average, find the number of events that should take place every day.
(b) Assuming the fission to take place largely through 235U, at what rate will the amount of 235U decrease? Express your answer in kg per day.
(c) Assuming that uranium enriched to 3% in 235U will be used, how much uranium is needed per month (30 days)?