Q. 13.31 Suppose India had a target of producing by 2020 AD, 200,000 MW of electric power, ten percent of which was to be obtained from nuclear power plants. Suppose we are given that, on an average, the efficiency of utilization (i.e. conversion to electric energy) of thermal energy produced in a reactor was 25%. How much amount of fissionable uranium would our country need per year by 2020? Take the heat energy per fission of 235U to be about 200MeV.
Q. 13.30 Calculate and compare the energy released by a) fusion of 1.0 kg of hydrogen deep within Sun and b) the fission of 1.0 kg of 235U in a fission reactor.
Q. 13.29 Obtain the maximum kinetic energy of - particles, and the radiation frequencies of decays in the decay scheme shown in Fig. 13.6. You are given that
Q.13.28 (b) Consider the D–T reaction (deuterium–tritium fusion)
(b) Consider the radius of both deuterium and tritium to be approximately 2.0 fm. What is the kinetic energy needed to overcome the coulomb repulsion between the two nuclei? To what temperature must the gas be heated to initiate the reaction? (Hint: Kinetic energy required for one fusion event =average thermal kinetic energy available with the interacting particles ; k = Boltzman’s constant, T = absolute temperature.)
Q.13.28 (i) Consider the D–T reaction (deuterium-tritium fusion)
(a) Calculate the energy released in MeV in this reaction from the data:
Q.13.27 Consider the fission of by fast neutrons. In one fission event, no neutrons are emitted and the final end products, after the beta decay of the primary fragments, are and . Calculate Q for this fission process. The relevant atomic and particle masses are
Q.13.26 Under certain circumstances, a nucleus can decay by emitting a particle more massive than an -particle. Consider the following decay processes:
Calculate the Q-values for these decays and determine that both are energetically allowed.
Q.13.25 A source contains two phosphorous radio nuclides and . Initially, 10% of the decays come from . How long one must wait until 90% do so?
Q.13.24 (ii) The neutron separation energy is defined as the energy required to remove a neutron from the nucleus. Obtain the neutron separation energies of the nuclei from the following data:
Q.13.24 (i) The neutron separation energy is defined as the energy required to remove a neutron from the nucleus. Obtain the neutron separation energies of the nuclei from the following data:
Q.13.23 In a periodic table the average atomic mass of magnesium is given as 24.312 u. The average value is based on their relative natural abundance on earth. The three isotopes and their masses are , and . The natural abundance of is 78.99% by mass. Calculate the abundances of other two isotopes.
Q. 13.22 For the (positron) emission from a nucleus, there is another competing process known as electron capture (electron from an inner orbit, say, the K–shell, is captured by the nucleus and a neutrino is emitted).
Show that if emission is energetically allowed, electron capture is necessarily allowed but not vice–versa.
Q. 13.21 From the relation , where is a constant and A is the mass number of a nucleus, show that the nuclear matter density is nearly constant (i.e. independent of A).
Q. 13.20 Calculate the height of the potential barrier for a head on collision of two deuterons. (Hint: The height of the potential barrier is given by the Coulomb repulsion between the two deuterons when they just touch each other. Assume that they can be taken as hard spheres of radius 2.0 fm.)
Q. 13.19 How long can an electric lamp of 100W be kept glowing by fusion of 2.0 kg of deuterium? Take the fusion reaction as
Q. 13.18 A fission reactor consumes half of its fuel in. How much did it contain initially? Assume that the reactor operates of the time, that all the energy generated arises from the fission of and that this nuclide is consumed only by the fission process.
Q. 13.17 The fission properties of are very similar to those of . The average energy released per fission is 180 MeV. How much energy, in MeV, is released if all the atoms in 1 kg of pure undergo fission?
Q.13.16 Suppose, we think of fission of a nucleus into two equal fragments, . Is the fission energetically possible? Argue by working out Q of the process. Given and
Q. 13.15 (ii) The Q value of a nuclear reaction is defined by where the masses refer to the respective nuclei. Determine from the given data the Q-value of the following reactions and state whether the reactions are exothermic or endothermic.
Atomic masses are given to be
Q. 13.15 (i) The Q value of a nuclear reaction is defined by where the masses refer to the respective nuclei. Determine from the given data the Q-value of the following reactions and state whether the reactions are exothermic or endothermic.
Atomic masses are given to be