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Physics · Textbook solutions

Nuclei

Every solved example, exercise, and miscellaneous question — in the order the textbook teaches them. · 15 questions

Worked Examples

4 q

Solved Examples

Worked · 4
  1. Eg 13.1
    Given the mass of iron nucleus as 55.85 u55.85\,\text{u} and A=56A = 56, find the nuclear density?
  2. Eg 13.2
    Calculate the energy equivalent of 1 g1\,\text{g} of substance.
  3. Eg 13.3
    Find the energy equivalent of one atomic mass unit, first in Joules and then in MeV. Using this, express the mass defect of 816O^{16}_{8}\text{O} in MeV/c2\text{MeV}/c^{2}.
  4. Eg 13.4
    Answer the following questions: (a) Are the equations of nuclear reactions (such as those given in Section 13.7) 'balanced' in the sense a chemical equation (e.g., 2H2+O2→2 H2O2\text{H}_2 + \text{O}_2 \rightarrow 2\,\text{H}_2\text{O}) is? If not, in what sense are they balanced on both sides? (b) If both the number of protons and the number of neutrons are conserved in each nuclear reaction, in what way is mass converted into energy (or vice-versa) in a nuclear reaction? (c) 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.

Exercises

11 q
  1. Ex 13.1
    Obtain the binding energy (in MeV) of a nitrogen nucleus (714N)\left({}^{14}_{7}\text{N}\right), given m(714N)=14.00307 um\left({}^{14}_{7}\text{N}\right) = 14.00307\,\text{u}.
  2. Ex 13.2
    Obtain the binding energy of the nuclei 2656Fe{}^{56}_{26}\text{Fe} and 83209Bi{}^{209}_{83}\text{Bi} in units of MeV from the following data: m(2656Fe)=55.934939 um({}^{56}_{26}\text{Fe}) = 55.934939\,\text{u} m(83209Bi)=208.980388 um({}^{209}_{83}\text{Bi}) = 208.980388\,\text{u}
  3. Ex 13.3
    A given coin has a mass of 3.0 g3.0\,\text{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 2963Cu{}^{63}_{29}\text{Cu} atoms (of mass 62.92960 u62.92960\,\text{u}).
  4. Ex 13.4
    Obtain approximately the ratio of the nuclear radii of the gold isotope 79197Au{}^{197}_{79}\text{Au} and the silver isotope 47107Ag{}^{107}_{47}\text{Ag}.
  5. Ex 13.5(i)
    The QQ value of a nuclear reaction A+b→C+dA + b \to C + d is defined by Q=[ mA+mb−mC−md ]c2Q = [\,m_A + m_b - m_C - m_d\,]c^2 where the masses refer to the respective nuclei. Determine from the given data the QQ-value of the following reaction and state whether the reaction is exothermic or endothermic. (i) 11H+13H→12H+12H{}^{1}_{1}\text{H} + {}^{3}_{1}\text{H} \to {}^{2}_{1}\text{H} + {}^{2}_{1}\text{H} Atomic masses are given to be m(12H)=2.014102 um({}^{2}_{1}\text{H}) = 2.014102\,\text{u} m(13H)=3.016049 um({}^{3}_{1}\text{H}) = 3.016049\,\text{u} m(612C)=12.000000 um({}^{12}_{6}\text{C}) = 12.000000\,\text{u} m(1020Ne)=19.992439 um({}^{20}_{10}\text{Ne}) = 19.992439\,\text{u}
  6. Ex 13.5(ii)
    The QQ value of a nuclear reaction A+b→C+dA + b \to C + d is defined by Q=[ mA+mb−mC−md ]c2Q = [\,m_A + m_b - m_C - m_d\,]c^2 where the masses refer to the respective nuclei. Determine from the given data the QQ-value of the following reaction and state whether the reaction is exothermic or endothermic. (ii) 612C+612C→1020Ne+24He{}^{12}_{6}\text{C} + {}^{12}_{6}\text{C} \to {}^{20}_{10}\text{Ne} + {}^{4}_{2}\text{He} Atomic masses are given to be m(12H)=2.014102 um({}^{2}_{1}\text{H}) = 2.014102\,\text{u} m(13H)=3.016049 um({}^{3}_{1}\text{H}) = 3.016049\,\text{u} m(612C)=12.000000 um({}^{12}_{6}\text{C}) = 12.000000\,\text{u} m(1020Ne)=19.992439 um({}^{20}_{10}\text{Ne}) = 19.992439\,\text{u}
  7. Ex 13.6
    Suppose, we think of fission of a 2656Fe{}^{56}_{26}\text{Fe} nucleus into two equal fragments, 1328Al{}^{28}_{13}\text{Al}. Is the fission energetically possible? Argue by working out QQ of the process. Given m(2656Fe)=55.93494 um({}^{56}_{26}\text{Fe}) = 55.93494\,\text{u} and m(1328Al)=27.98191 um({}^{28}_{13}\text{Al}) = 27.98191\,\text{u}.
  8. Ex 13.7
    The fission properties of 94239Pu{}^{239}_{94}\text{Pu} are very similar to those of 92235U{}^{235}_{92}\text{U}. The average energy released per fission is 180 MeV180\,\text{MeV}. How much energy, in MeV, is released if all the atoms in 1 kg1\,\text{kg} of pure 94239Pu{}^{239}_{94}\text{Pu} undergo fission?
  9. Ex 13.8
    How long can an electric lamp of 100 W100\,\text{W} be kept glowing by fusion of 2.0 kg2.0\,\text{kg} of deuterium? Take the fusion reaction as 12H+12H→23He+n+3.27 MeV{}^{2}_{1}\text{H} + {}^{2}_{1}\text{H} \to {}^{3}_{2}\text{He} + \text{n} + 3.27\,\text{MeV}
  10. Ex 13.9
    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 fm2.0\,\text{fm}.)
  11. Ex 13.10
    From the relation R=R0A1/3R = R_0 A^{1/3}, where R0R_0 is a constant and AA is the mass number of a nucleus, show that the nuclear matter density is nearly constant (i.e. independent of AA).