# NCERT Solutions for class 12th Physics Chapter 13 Nuclei

#### Exercise

Question 1. (a) Two stable isotopes of lithium 6,3Li and 7,3Li have respective abundances of 7.5% and 92.5%. These isotopes have masses 6.01512 u and 7.01600 u respectively. Find the atomic mass of lithium.

(b) Boron has two stable isotopes, 10,5B and 11,5B. Their respective masses are 10.01294 u and 11.00931u, and the atomic mass of boron is 10.811u. Find the abundances of 10,5B and 11,5 B.

Question 2. The three stable isotopes of neon: 20,10Ne, 21,10Ne and 22,10 Ne have respective abundances of 90.51%, 0.27% and 9.22%. The atomic masses of the three isotopes are 19.99 u, 20.99 u and 21.99 u, respectively. Obtain the average atomic mass of neon.

Question 3. Obtain the binding energy (in MeV) of a nitrogen nucleus( 14,7N), given m(14,7N) = 14.00307 u

Note: If one wants to break nitrogen nucleus into its constituents (protons and neutrons),
this much extra energy has to be supplied.

Question 4. Obtain the binding energy of the nuclei (56,26Fe) and 209,83 Bi in units of MeV from the following data :

Question 5. A given coin has a mass of 3.0 g. Calculate the nuclear energy that would be required to separate all the neutrons and protons from each other. For simplicity assume that the coin is entirely made of 63,29 Cu atoms (of mass 62.92960 u)

Question 6. Write nuclear reaction equations for

Question 7. A radioactive isotope has a half-life of T years. How long will it take the activity to reduce to a) 3.125%, b) 1% of its original value?

Note: Refer Chapter at a Glance (15)

Question 8. The normal activity of living carbon-containing matter is found to be about 15 decays per minute for every gram of carbon. This activity arises from the small proportion of radioactive 14,6 C present with the stable carbon isotope 12,6 C when the organism is dead, its interaction with the atmosphere (which maintains the above equilibrium activity) ceases and its activity begins to drop. From the known halflives of 14,6C,and the measured activity, the age of the specimen can be approximately estimated. This is the principle of 14,6 C dating used in archaeology. Suppose a specimen from Mohenjodaro gives an activity of 9 decays per minute per gram of carbon. Estimate the approximate age of the Indus-Valley civilisation.

Question 9. Obtain the amount of 60,27 Co necessary to provide a radioactive source of 8.0m Ci strength.The half-life of 60,27 Co is 5.3 years.

Question 10. The half-life of 90,38 Sr is 28 years. What is the disintegration rate of 15 mg of this isotope?

Question 11. Obtain approximately the ratio of the nuclear radii of the gold isotope 197,79 Au and the silver isotope 107,47 Ag.

Question 12. Find the Q-value and the kinetic energy of the emitted a -particle in the a – decay of

Note: This Q value is also the net kinetic energy gained in the process.

Question 13. The radionuclide 11C decays according to

Question 14. The nucleus 23,10 Ne decays by 13-emission. Write down the beta-decay equation and determine the maximum kinetic energy of the electrons emitted. Given that:

Question 15. The Q value of an uclear reaction A+b–> C+d is defined by Q=[mA+mb-mc-md]c2
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.

Question 16. Suppose, we think of fission of a (56,26)Fe nucleus into two equal fragments,(28,13) Al. Is the fission energetically possible? Argue by working out Q of the process. Given m(56,26)Fe = 55.93494 amu and m (28,13 Al) = 27.98191 amu.

Question 17. The fission properties of 239,94 Pu are very similar to those of (235,92)U. 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 (239,94)Pu undergo fission?

Question 18. A 1000 MW fission reactor consumes half of its fuel in 5.00 y. How much (235,92)U did it contain initially? Assume that the reactor operates 80% of the time, that all the energy generated arises from the fission of (235,92)U and that this nuclide is consumed only by the fission process.

Question 19. How long can an electric lamp of l00W be kept glowing by fusion of 2.0 kg of deuterium? Take the fusion reaction as

Question 20. Calculate the height of the potential barrier for a head on collision of two deuterons. The effective radius of deuteron can be taken to be 2 fm. Note that height of potential barrier is given by the Coulomb repulsion between two deuterons when they just touch each other

Note: It shall be noted that unloke coulomb force (between say two deutrons), nuclear forces are both repulsive (when they one near) and attractive ( when nucleons one far).

Question 21. 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 (i.e.independent of A).

Question 22. For the Beta+ (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).

Question 23. In a periodic table the average atomic mass of magnesium is given as 24.312u. The average value is based on their relative natural abundance on earth.

Question 24. 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 (41,20)Ca and (77.13)Al from the following data:

Question 25. A source contains two phosphorous radio nuclides(32,15)P(T1/2 = 14.3d) and (33,15)P(T1/2 = 25.3d). Initially, 10% of the decays come from (33,15)P. How long one must wait until (33,15)P do so?

Question 26. Under certain circumstances, a nucleus can decay by emitting a particle more massive than an a-particle. Consider the following decay processes:

Calculate the Q-values for these decays and determine that both are energetically allowed.

Question 27. Consider the fission of (238,92)U 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 (140,58)Ce and (99,44)Ru. Calculate Q for this fission process. The relevant atomic and particle masses are

Question 28. (a) Consider the D-T reaction (deuterium-tritium fusion)

Calculate the energy released in MeVin this reaction from the data:

(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’s constant, T = absolute temperature.)

Note: This required temerature is very large. Compare this with the temerature in core of star (The interior of sun has a temerature of 1.5 x 107K).

Question 29. Obtain the maximum kinetic energy of Beta-particles, and the radiation frequencies of y- decays in the decay scheme shown in fig. You are given that

Note: In gamma decay, the energy corresponds to the radiation of extremely short wavelength. Which is smaller than the hard x-ray region.

Question 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 of235U in a fission reactor.

Note: Fusion can be achieved by raising the temperature of the system, so that the particles have sufficient energy to overcome coulomb repulsion. This is called thermo nuclear fusion.

Question 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 200 MeV.

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