Chapter 13 Solutions — Nuclei

Exercises

1. 1.
   Obtain the binding energy (in MeV) of a nitrogen nucleus (14_7 N), given m(14_7 N) = 14.00307 u.
2. 2.
   Obtain the binding energy of the nuclei 56_26 Fe and 209_83 Bi in units of MeV from the following data: m(56_26 Fe) = 55.934939 u, m(209_83 Bi) = 208.980388 u.
3. 3.
   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).
4. 4.
   Obtain approximately the ratio of the nuclear radii of the gold isotope 197_79 Au and the silver isotope 107_47 Ag.
5. 5.
   The Q value of a nuclear reaction A + b -> C + d is defined by Q = [m_A + m_b - m_C - m_d]c^2 where the masses refer to the respective nuclei. Determine the Q-value of the following reactions and state whether the reactions are exothermic or endothermic.

   • (i) 1_1 H + 3_1 H -> 2_1 H + 2_1 H
   • (ii) 12_6 C + 12_6 C -> 20_10 Ne + 4_2 He Atomic masses: m(2_1 H) = 2.014102 u, m(3_1 H) = 3.016049 u…
6. 6.
   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 u and m(28_13 Al) = 27.98191 u.
7. 7.
   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?
8. 8.
   How long can an electric lamp of 100 W be kept glowing by fusion of 2.0 kg of deuterium? Take the fusion reaction as 2_1 H + 2_1 H -> 3_2 He + n + 3.27 MeV.
9. 9.
   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.)
10. 10.
    From the relation R = R_0 A^(1/3), where R_0 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).