1.Suppose, we think of fission of a nucleus into two equal fragments, . Is the fission energetically possible? Argue by working out of the process. Given
The supposed nuclear reaction is
As the value of Q is negative the fission is energetically not possible.
2.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?
According to mole concept,
3.A 1000 MW fission reactor consumes half of its fuel in 5.00 years. How much did it contain initially? Assume that the reactor operates 80% of the time, that all the energy generated arises from the fission of and that this nuclide is consumed only by the fission process.
4.How long can an electric lamp of 100 W be kept glowing by fusion of 2.0 kg deuterium? Take the fusion reaction as
5.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.)
The potential energy of a system of two deuterons when they almost touch each other
6.From the relation R = R0A1/3, where R0 is a constant and A is the mass number of a nucleus, show that the nuclear matter density is nearly constant (that is independent of A).
7.For the β+ (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 β+ emission is energetically allowed, electron capture is necessarily allowed but not vice versa.
Thus, we may conclude that if β+ emission is energetically allowed, electron capture is necessarily allowed but not vice versa.
8.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 (23.98504 u), (24.98584 u) and (25.98259 u). The natural abundance of is 78.99% by mass. Calculate the abundances of other two isotopes.
9.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
10.A source contains two phosphorus radio nuclides Initially, 10% of the decays come from How long one must wait until 90% do so?
11.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.
12.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 Calculate Q for this fission process. The relevant atomic and particle masses are
13.Heavy water is a suitable moderator for nuclear reactor. Why?
By fission of uranium in the reactor, fast moving neutrons are produced. To continue the chain reaction of the fission by these neutrons, they must be slowed down. For this they are made to collide with some moderator. The moderator will be most effective in slowing down the neutrons, if the mass of its nucleus is almost of the same order as that of the neutrons. If the nuclei of moderator are very heavy, the neutrons will go back on its path after colliding with it and if the nuclei are light, the neutron will move forwarded after striking with them. The mass of the heavy water nucleus is of the order as that of the neutrons. Hence they are most suitable to slow down the fast neutrons.
14.Why ionic compounds have high melting point?
Oppositely charged ions are tightly bound by strong electrostatic force of attraction in ionic compounds. So a large heat energy is required to break these bonds.
15. A general impression exists that mass-energy interconversion takes place only in nuclear reaction and never in chemical reaction. This is strictly speaking incorrect. Explain?
Strictly speaking, mass defect is applicable in the case of chemical reactions but it is nearly only millionth times smaller than that in nuclear reaction so practically it can be said that the mass defect has non significance in the case of chemical reactions.
16.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 = 2(3kT/2); k = Boltzmann constant, T = absolute temperature.]
17.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.
In the fusion reaction going on in sun four hydrogen atoms combine to form a atom with a release of 26.7 MeV of energy. The number of hydrogen atoms in 1 kg (1000 g) of hydrogen
18.Suppose India has a target of producing by 2020 AD, 200,000 MW of electric power, ten per cent 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 MeV