Chemistry · Textbook solutions

Nuclear Chemistry and Radioactivity

Every solved example, exercise, and miscellaneous question — in the order the textbook teaches them. · 54 questions

13. Nuclear Chemistry and Radioactivity — worked examples

8 q

Solved Examples

Worked · 8
  1. Solved Ex.13.1
    Calculate the mean binding energy per nucleon for the formation of 816O^{16}_{8}\mathrm{O} nucleus. The mass of oxygen atom is 15.994 u. The masses of H atom and neutron are 1.0078 u and 1.0087 u, respectively.
  2. Solved Ex.13.2
    41Ar^{41}\mathrm{Ar} decays initially at a rate of 575 Bq. The rate falls to 358 dps after 75 minutes. What is the half life of 41Ar^{41}\mathrm{Ar}?
  3. Solved Ex.13.3
    The half life of 32P^{32}\mathrm{P} is 14.26 d. What percentage of 32P^{32}\mathrm{P} sample will remain after 40 d?
  4. Solved Ex.13.4
    The half life of 34Cl^{34}\mathrm{Cl} is 1.53 s. How long does it take for 99.9 % of sample of 34Cl^{34}\mathrm{Cl} to decay?
  5. Solved Ex.13.5
    The half life of 209Po^{209}\mathrm{Po} is 102 y. How much of 1 mg sample of polonium decays in 62 y?
  6. Solved Ex.13.6
    How many α\alpha and β\beta- particles are emitted in the following? 93237Np⟶83209Bi^{237}_{93}\mathrm{Np} \longrightarrow{} ^{209}_{83}\mathrm{Bi}
  7. Solved Ex.13.7
    Estimate the energy released in the fusion reaction 12H+23He⟶24He+11H^{2}_{1}\mathrm{H} + {}^{3}_{2}\mathrm{He} \longrightarrow {}^{4}_{2}\mathrm{He} + {}^{1}_{1}\mathrm{H} Given atomic masses : 2H^{2}\mathrm{H} = 2.041 u, 3He^{3}\mathrm{He} = 3.0160 u, 4He^{4}\mathrm{He} = 4.0026 u, 1H^{1}\mathrm{H} = 1.0078 u
  8. Solved Ex.13.8
    Half life of 209Po^{209}\mathrm{Po} is 102 y. How many α\alpha-particles are emitted in 1 s from 2 mg sample of Po?

Exercises

46 q

1. Choose correct option.

Practice · 5
  1. Choose correct option.
    Ex Q.1 (A)
    Identify nuclear fusion reaction a. 11H+11H⟶12H+10e^{1}_{1}\mathrm{H} + {}^{1}_{1}\mathrm{H} \longrightarrow {}^{2}_{1}\mathrm{H} + {}^{0}_{1}\mathrm{e} b. 12H+11H⟶23He^{2}_{1}\mathrm{H} + {}^{1}_{1}\mathrm{H} \longrightarrow {}^{3}_{2}\mathrm{He} c. 13H+11H⟶13H+11p^{3}_{1}\mathrm{H} + {}^{1}_{1}\mathrm{H} \longrightarrow {}^{3}_{1}\mathrm{H} + {}^{1}_{1}\mathrm{p}
  2. Ex Q.1 (B)
    The missing particle from the nuclear reaction is 1327Al+24He⟶ ?+01n^{27}_{13}\mathrm{Al} + {}^{4}_{2}\mathrm{He} \longrightarrow\ ? + {}^{1}_{0}\mathrm{n}
    1. A.
      1530P^{30}_{15}\mathrm{P}
    2. B.
      1632S^{32}_{16}\mathrm{S}
    3. C.
      1014Ne^{14}_{10}\mathrm{Ne}
    4. D.
      14Si_{14}\mathrm{Si}
  3. Ex Q.1 (C)
    2760CO^{60}_{27}\mathrm{CO} decays with half-life of 5.27 years to produce 2860Ni^{60}_{28}\mathrm{Ni}. What is the decay constant for such radioactive disintegration?
    1. A.
      0.132 y−10.132\ \mathrm{y^{-1}}
    2. B.
      0.138
    3. C.
      29.6 y
    4. D.
      13.8%
  4. Ex Q.1 (D)
    The radioactive isotope used in the treatment of Leukemia is
    1. A.
      60Co^{60}\mathrm{Co}
    2. B.
      226Ra^{226}\mathrm{Ra}
    3. C.
      32P^{32}\mathrm{P}
    4. D.
      226I^{226}\mathrm{I}
  5. Ex Q.1 (E)
    The process by which nuclei having low masses are united to form nuclei with large masses is
    1. A.
      chemical reaction
    2. B.
      nuclear fission
    3. C.
      nuclear fusion
    4. D.
      chain reaction

2. Explain

Practice · 10
  1. Explain
    Ex Q.2 (A)
    On the basis of even-odd of protons and neutrons, what type of nuclides are most stable?
  2. Ex Q.2 (B)
    Explain in brief, nuclear fission.
  3. Ex Q.2 (C)
    The nuclides with odd number of both protons and neutrons are the least stable. Why?
  4. Ex Q.2 (D)
    Referring the stabilty belt of stable nuclides, which nuclides are β−\beta^{-} and β+\beta^{+} emitters? Why?
  5. Ex Q.2 (E)
    Explain with an example each nuclear transmutation and artifiacial radioactivity. What is the difference between them?
  6. Ex Q.2 (F)
    What is binding energy per nucleon? Explain with the help of diagram how binding energy per nucleon affects nuclear stability?
  7. Ex Q.2 (G)
    Explain with example α\alpha - decay.
  8. Ex Q.2 (H)
    Energy produced in nuclear fusion is much larger than that produced in nuclear fission. Why is it difficult to use fusion to produce energy?
  9. Ex Q.2 (I)
    How does N/ZN/Z ratio affect the nuclear stability? Explain with a suitable diagram.
  10. Ex Q.2 (J)
    You are given a very old sample of wood. How will you determine its age?

3. Answer the following question

Practice · 18
  1. Answer the following question
    Ex Q.3 (A)
    Give example of mirror nuclei.
  2. Ex Q.3 (B)
    Balance the nuclear reaction: 54118Xe⟶ ?+I54118^{118}_{54}\mathrm{Xe} \longrightarrow\ ? + \mathrm{I}^{118}_{54}
  3. Ex Q.3 (C)
    Name the most stable nluclide known. Write two factors responsible for its stability.
  4. Ex Q.3 (D)
    Write relation between decay constant of a radioelement and its half life.
  5. Ex Q.3 (E)
    What is the difference between an α\alpha - particle and helium atom?
  6. Ex Q.3 (F)
    Write one point that differentiates nuclear reations from chemical reactions.
  7. Ex Q.3 (G)
    Write pairs of isotones and one pair of mirror nuclei from the following : 510B^{10}_{5}\mathrm{B}, 612C^{12}_{6}\mathrm{C}, 1327Al^{27}_{13}\mathrm{Al}, 611C^{11}_{6}\mathrm{C}, 1428S^{28}_{14}\mathrm{S}:
  8. Ex Q.3 (H)
    Derive the relationship between half life and decay constant of a radioelement.
  9. Ex Q.3 (I)
    Represent graphically log⁡10\log_{10} (activity / dps) versus t/st/\mathrm{s}. What is its slope?
  10. Ex Q.3 (J)
    Write two units of radioactivity. How are they interrelated?
  11. Ex Q.3 (K)
    Half life of 24Na^{24}\mathrm{Na} is 900 minutes. What is its decay constant?
  12. Ex Q.3 (L)
    Decay constant of 197Hg^{197}\mathrm{Hg} is 0.017 h−10.017\ \mathrm{h^{-1}}. What is its half life?
  13. Ex Q.3 (M)
    The total binding energy of 58Ni^{58}\mathrm{Ni} is 508 MeV. What is its binding energy per nucleon?
  14. Ex Q.3 (N)
    Atomic mass of 1632S^{32}_{16}\mathrm{S} is 31.97 u. If masses of neutron and H atom are 1.0087 u and 1.0078 u respectively. What is the mass defect?
  15. Ex Q.3 (O)
    Write the fusion reactions occuring in the Sun and stars.
  16. Ex Q.3 (P)
    How many α\alpha and β\beta - particles are emitted in the trasmutation 90232Th⟶82208Pb^{232}_{90}\mathrm{Th} \longrightarrow {}^{208}_{82}\mathrm{Pb} ?
  17. Ex Q.3 (Q)
    A produces B by α\alpha- emission. If B is in the group 16 of periodic table, what is the group of A?
  18. Ex Q.3 (R)
    Find the number of α\alpha and β\beta- particles emitted in the process 86222Rn⟶84214Po^{222}_{86}\mathrm{Rn} \longrightarrow {}^{214}_{84}\mathrm{Po}

4. Solve the problems

Practice · 13
  1. Solve the problems
    Ex Q.4 (A)
    Half life of 18F^{18}\mathrm{F} is 110 minutes. What fraction of 18F^{18}\mathrm{F} sample decays in 20 minutes?
  2. Ex Q.4 (B)
    Half life of 35S^{35}\mathrm{S} is 87.8 d. What percentage of 35S^{35}\mathrm{S} sample remains after 180 d?
  3. Ex Q.4 (C)
    Half life 67Ga^{67}\mathrm{Ga} is 78 h. How long will it take to decay 12% of sample of Ga?
  4. Ex Q.4 (D)
    0.5 g Sample of 201Tl^{201}\mathrm{Tl} decays to 0.0788 g in 8 days. What is its half life?
  5. Ex Q.4 (E)
    65% of 111In^{111}\mathrm{In} sample decays in 4.2 d. What is its half life?
  6. Ex Q.4 (F)
    Calculate the binding energy per nucleon of 3684Kr^{84}_{36}\mathrm{Kr} whose atomic mass is 83.913 u. (Mass of neutron is 1.0087 u and that of H atom is 1.0078 u).
  7. Ex Q.4 (G)
    Calculate the energy in Mev released in the nuclear reaction 77174Ir⟶75170Re+24He^{174}_{77}\mathrm{Ir} \longrightarrow {}^{170}_{75}\mathrm{Re} + {}^{4}_{2}\mathrm{He} Atomic masses : Ir = 173.97 u, Re = 169.96 u and He = 4.0026 u
  8. Ex Q.4 (H)
    A 3/4 of the original amount of radioisotope decays in 60 minutes. What is its half life?
  9. Ex Q.4 (I)
    How many - particles are emitted by 0.1 g of 226Ra^{226}\mathrm{Ra} in one year?
  10. Ex Q.4 (J)
    A sample of 32P^{32}\mathrm{P} initially shows activity of one Curie. After 303 days the activity falls to 1.5×1041.5 \times 10^{4} dps. What is the half life of 32P^{32}\mathrm{P}?
  11. Ex Q.4 (K)
    Half life of radon is 3.82 d. By what time would 99.9 % of radon will be decayed.
  12. Ex Q.4 (L)
    It has been found that the Sun's mass loss is 4.34×1094.34 \times 10^{9} kg per second. How much energy per second would be radiated into space by the Sun?
  13. Ex Q.4 (M)
    A sample of old wood shows 7.0 dps/g. If the fresh sample of tree shows 16.0 dps/g, How old is the given sample of wood? Half life of 14C^{14}\mathrm{C} 5730 y.