Nuclear Physics Problems

This section provides 100 problems to test your understanding of nuclear physics, including calculations of binding energy, mass defect, decay constants, half-life, Q-values, and reaction rates, as well as applications like carbon dating and nuclear propulsion in spacecraft. Inspired by JEE Main, JEE Advanced, and NEET exam patterns, these problems are tailored for exam preparation, offering a mix of numerical, conceptual, and derivation-based challenges. NEET-style problems (66–100) are formatted as multiple-choice questions (MCQs) to match the exam’s objective format. Problems are organized by type to support progressive learning and build confidence in mastering nuclear physics, a key topic for JEE/NEET success.

Numerical Problems

1. Calculate the mass defect of ${}_2^4\text{He}$ (in u). Given: $m{(}_2^4\text{He})=4.002602\text{u}$, $m_p=1.007825\text{u}$, $m_n=1.008665\text{u}$.

   • (a) 0.03037 u
   • (b) 0.03038 u
   • (c) 0.03039 u
   • (d) 0.03040 u

2. Calculate the binding energy per nucleon of ${}_6^{12}\text{C}$ in MeV. Given: $m{(}_6^{12}\text{C})=12.000000\text{u}$, $m_p=1.007825\text{u}$, $m_n=1.008665\text{u}$, $c^2=931.494\text{MeV/u}$.

   • (a) 7.67 MeV
   • (b) 7.68 MeV
   • (c) 7.69 MeV
   • (d) 7.70 MeV

3. A radioactive sample has a half-life of 3 days. If the initial activity is 800 Bq, calculate the activity after 9 days in Bq.

   • (a) 99 Bq
   • (b) 100 Bq
   • (c) 101 Bq
   • (d) 102 Bq

4. Calculate the Q-value of the reaction ${}_1^2\text{H}{+}_1^3\text{H}{\to }_2^4\text{He}{+}_0^1\text{n}$ in MeV. Given: $m{(}_1^2\text{H})=2.0141\text{u}$, $m{(}_1^3\text{H})=3.0160\text{u}$, $m{(}_2^4\text{He})=4.0026\text{u}$, $m{(}_0^1\text{n})=1.0087\text{u}$.

   • (a) 17.50 MeV
   • (b) 17.51 MeV
   • (c) 17.52 MeV
   • (d) 17.53 MeV

5. A sample of ${}^{14}\text{C}$ has an activity 1/16 of a living sample ($T_{1/2}=5730\text{years}$). Calculate the age of the sample in years.

   • (a) 22918
   • (b) 22919
   • (c) 22920
   • (d) 22921

6. A nuclear reactor produces 2 MW of power. If each fission releases 200 MeV, calculate the number of fissions per second.

   • (a) $6.24\times {10}^{16}$
   • (b) $6.25\times {10}^{16}$
   • (c) $6.26\times {10}^{16}$
   • (d) $6.27\times {10}^{16}$

7. Calculate the binding energy of ${}_8^{16}\text{O}$ in MeV. Given: $m{(}_8^{16}\text{O})=15.994915\text{u}$, $m_p=1.007825\text{u}$, $m_n=1.008665\text{u}$.

   • (a) 127.60 MeV
   • (b) 127.61 MeV
   • (c) 127.62 MeV
   • (d) 127.63 MeV

8. A radioactive isotope has a decay constant $\lambda =0.02{\text{s}}^{-1}$ and initial number of nuclei $N_0={10}^9$. Calculate the activity after 50 s in Bq.

   • (a) $7.36\times {10}^7$
   • (b) $7.37\times {10}^7$
   • (c) $7.38\times {10}^7$
   • (d) $7.39\times {10}^7$

9. Calculate the Q-value of ${}_7^{14}\text{N}{+}_0^1\text{n}{\to }_6^{14}\text{C}{+}_1^1\text{H}$ in MeV. Given: $m{(}_7^{14}\text{N})=14.0031\text{u}$, $m{(}_0^1\text{n})=1.0087\text{u}$, $m{(}_6^{14}\text{C})=14.0032\text{u}$, $m{(}_1^1\text{H})=1.0078\text{u}$.

   • (a) 0.74 MeV
   • (b) 0.75 MeV
   • (c) 0.76 MeV
   • (d) 0.77 MeV

10. A sample has $T_{1/2}=4\text{years}$, initial activity 1600 Bq. Calculate the activity after 8 years in Bq.

    • (a) 399 Bq
    • (b) 400 Bq
    • (c) 401 Bq
    • (d) 402 Bq

11. Calculate the binding energy per nucleon of ${}_2{6}^{56}\text{Fe}$ in MeV. Given: $m{(}_2{6}^{56}\text{Fe})=55.9349\text{u}$, $m_p=1.007825\text{u}$, $m_n=1.008665\text{u}$.

    • (a) 8.78 MeV
    • (b) 8.79 MeV
    • (c) 8.80 MeV
    • (d) 8.81 MeV

12. A radioactive sample has $\lambda =0.01{\text{s}}^{-1}$, $N_0={10}^{10}$. Calculate $N$ after 100 s.

    • (a) $3.67\times {10}^9$
    • (b) $3.68\times {10}^9$
    • (c) $3.69\times {10}^9$
    • (d) $3.70\times {10}^9$

13. Calculate the Q-value of ${}_1^2\text{H}{+}_1^2\text{H}{\to }_2^3\text{He}{+}_0^1\text{n}$ in MeV. Given: $m{(}_1^2\text{H})=2.0141\text{u}$, $m{(}_2^3\text{He})=3.0160\text{u}$, $m{(}_0^1\text{n})=1.0087\text{u}$.

    • (a) 3.26 MeV
    • (b) 3.27 MeV
    • (c) 3.28 MeV
    • (d) 3.29 MeV

14. A sample has $T_{1/2}=5\text{days}$, initial $N_0={10}^{12}$. Calculate $N$ after 10 days.

    • (a) $2.49\times {10}^{11}$
    • (b) $2.50\times {10}^{11}$
    • (c) $2.51\times {10}^{11}$
    • (d) $2.52\times {10}^{11}$

15. Calculate the mass defect of ${}_9{2}^{238}\text{U}$ in u. Given: $m{(}_9{2}^{238}\text{U})=238.0508\text{u}$, $m_p=1.007825\text{u}$, $m_n=1.008665\text{u}$.

    • (a) 1.9340 u
    • (b) 1.9341 u
    • (c) 1.9342 u
    • (d) 1.9343 u

16. A radioactive isotope has $T_{1/2}=2\text{hours}$, initial activity 500 Bq. Calculate activity after 6 hours in Bq.

    • (a) 62.4 Bq
    • (b) 62.5 Bq
    • (c) 62.6 Bq
    • (d) 62.7 Bq

17. Calculate the binding energy of ${}_3^7\text{Li}$ in MeV. Given: $m{(}_3^7\text{Li})=7.0160\text{u}$, $m_p=1.007825\text{u}$, $m_n=1.008665\text{u}$.

    • (a) 39.24 MeV
    • (b) 39.25 MeV
    • (c) 39.26 MeV
    • (d) 39.27 MeV

18. A sample has $\lambda =0.005{\text{s}}^{-1}$, $N_0={10}^8$. Calculate $A$ after 200 s in Bq.

    • (a) $1.84\times {10}^5$
    • (b) $1.85\times {10}^5$
    • (c) $1.86\times {10}^5$
    • (d) $1.87\times {10}^5$

19. Calculate the Q-value of ${}_9{4}^{239}\text{Pu}{\to }_9{2}^{235}\text{U}{+}_2^4\text{He}$ in MeV. Given: $m{(}_9{4}^{239}\text{Pu})=239.0522\text{u}$, $m{(}_9{2}^{235}\text{U})=235.0439\text{u}$, $m{(}_2^4\text{He})=4.0026\text{u}$.

    • (a) 5.24 MeV
    • (b) 5.25 MeV
    • (c) 5.26 MeV
    • (d) 5.27 MeV

20. A sample has $T_{1/2}=10\text{years}$, initial $N_0={10}^{11}$. Calculate $N$ after 20 years.

    • (a) $2.49\times {10}^{10}$
    • (b) $2.50\times {10}^{10}$
    • (c) $2.51\times {10}^{10}$
    • (d) $2.52\times {10}^{10}$

21. Calculate the binding energy per nucleon of ${}_9{2}^{238}\text{U}$ in MeV (use mass defect from Problem 15).

    • (a) 7.57 MeV
    • (b) 7.58 MeV
    • (c) 7.59 MeV
    • (d) 7.60 MeV

22. A radioactive sample has $T_{1/2}=1\text{day}$, initial activity 2000 Bq. Calculate activity after 3 days in Bq.

    • (a) 249 Bq
    • (b) 250 Bq
    • (c) 251 Bq
    • (d) 252 Bq

23. Calculate the Q-value of ${}_6^{11}\text{C}{\to }_5^{11}\text{B}+e^{+}+{\nu }_e$ in MeV. Given: $m{(}_6^{11}\text{C})=11.0114\text{u}$, $m{(}_5^{11}\text{B})=11.0093\text{u}$, $m(e^{+})=0.00054858\text{u}$.

    • (a) 0.96 MeV
    • (b) 0.97 MeV
    • (c) 0.98 MeV
    • (d) 0.99 MeV

24. A sample has $\lambda =0.003{\text{s}}^{-1}$, $N_0={10}^7$. Calculate $N$ after 300 s.

    • (a) $4.06\times {10}^5$
    • (b) $4.07\times {10}^5$
    • (c) $4.08\times {10}^5$
    • (d) $4.09\times {10}^5$

25. Calculate the mass defect of ${}_7^{14}\text{N}$ in u. Given: $m{(}_7^{14}\text{N})=14.0031\text{u}$, $m_p=1.007825\text{u}$, $m_n=1.008665\text{u}$.

    • (a) 0.1123 u
    • (b) 0.1124 u
    • (c) 0.1125 u
    • (d) 0.1126 u

26. A radioactive isotope has $T_{1/2}=6\text{hours}$, initial $N_0={10}^{10}$. Calculate $N$ after 12 hours.

    • (a) $2.49\times {10}^9$
    • (b) $2.50\times {10}^9$
    • (c) $2.51\times {10}^9$
    • (d) $2.52\times {10}^9$

27. Calculate the binding energy of ${}_1^3\text{H}$ in MeV. Given: $m{(}_1^3\text{H})=3.0160\text{u}$, $m_p=1.007825\text{u}$, $m_n=1.008665\text{u}$.

    • (a) 8.47 MeV
    • (b) 8.48 MeV
    • (c) 8.49 MeV
    • (d) 8.50 MeV

28. A sample has $\lambda =0.008{\text{s}}^{-1}$, $N_0={10}^6$. Calculate $A$ after 125 s in Bq.

    • (a) $2.68\times {10}^3$
    • (b) $2.69\times {10}^3$
    • (c) $2.70\times {10}^3$
    • (d) $2.71\times {10}^3$

29. Calculate the Q-value of ${}_8{8}^{226}\text{Ra}{\to }_8{6}^{222}\text{Rn}{+}_2^4\text{He}$ in MeV. Given: $m{(}_8{8}^{226}\text{Ra})=226.0254\text{u}$, $m{(}_8{6}^{222}\text{Rn})=222.0176\text{u}$, $m{(}_2^4\text{He})=4.0026\text{u}$.

    • (a) 4.86 MeV
    • (b) 4.87 MeV
    • (c) 4.88 MeV
    • (d) 4.89 MeV

30. A sample has $T_{1/2}=15\text{years}$, initial activity 3200 Bq. Calculate activity after 30 years in Bq.

    • (a) 799 Bq
    • (b) 800 Bq
    • (c) 801 Bq
    • (d) 802 Bq

31. A spacecraft RTG uses ${}^{238}\text{Pu}$ with $T_{1/2}=87.7\text{years}$, activity 2 Ci. Calculate $\lambda$ in s${}^{-1}$.

    • (a) $2.49\times {10}^{-10}$
    • (b) $2.50\times {10}^{-10}$
    • (c) $2.51\times {10}^{-10}$
    • (d) $2.52\times {10}^{-10}$

32. Calculate the binding energy per nucleon of ${}_2{0}^{40}\text{Ca}$ in MeV. Given: $m{(}_2{0}^{40}\text{Ca})=39.9626\text{u}$, $m_p=1.007825\text{u}$, $m_n=1.008665\text{u}$.

    • (a) 8.54 MeV
    • (b) 8.55 MeV
    • (c) 8.56 MeV
    • (d) 8.57 MeV

33. A radioactive sample has $T_{1/2}=8\text{days}$, initial $N_0={10}^{15}$. Calculate $N$ after 16 days.

    • (a) $2.49\times {10}^{14}$
    • (b) $2.50\times {10}^{14}$
    • (c) $2.51\times {10}^{14}$
    • (d) $2.52\times {10}^{14}$

34. Calculate the Q-value of ${}_6^{14}\text{C}{\to }_7^{14}\text{N}+e^{-}+{\overline{\nu }}_e$ in MeV. Given: $m{(}_6^{14}\text{C})=14.0032\text{u}$, $m{(}_7^{14}\text{N})=14.0031\text{u}$, $m(e^{-})=0.00054858\text{u}$.

    • (a) 0.15 MeV
    • (b) 0.16 MeV
    • (c) 0.17 MeV
    • (d) 0.18 MeV

35. A sample has $T_{1/2}=20\text{years}$, initial activity 6400 Bq. Calculate activity after 40 years in Bq.

    • (a) 1599 Bq
    • (b) 1600 Bq
    • (c) 1601 Bq
    • (d) 1602 Bq

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Conceptual Problems

36. What does the mass number $A$ represent in a nucleus?

    • (a) Number of protons
    • (b) Number of neutrons
    • (c) Total number of nucleons
    • (d) Number of electrons

37. What type of decay does ${}_9{2}^{238}\text{U}{\to }_9{0}^{234}\text{Th}{+}_2^4\text{He}$ represent?

    • (a) Alpha decay
    • (b) Beta decay
    • (c) Gamma decay
    • (d) Fission

38. What is the unit of activity $A$ in SI units?

    • (a) Becquerel (Bq)
    • (b) Joule
    • (c) Hertz
    • (d) Watt

39. What happens to the activity of a radioactive sample after one half-life?

    • (a) Doubles
    • (b) Halves
    • (c) Remains the same
    • (d) Becomes zero

40. What type of reaction is ${}_1^2\text{H}{+}_1^3\text{H}{\to }_2^4\text{He}{+}_0^1\text{n}$?

    • (a) Fission
    • (b) Fusion
    • (c) Alpha decay
    • (d) Beta decay

41. What is the unit of binding energy $E_b$ commonly used in nuclear physics?

    • (a) MeV
    • (b) Joule
    • (c) Hertz
    • (d) Watt

42. What does a positive Q-value indicate about a nuclear reaction?

    • (a) Endothermic
    • (b) Exothermic
    • (c) No energy change
    • (d) Unstable reaction

43. What happens to the atomic number $Z$ in ${\beta }^{-}$ decay?

    • (a) Decreases by 1
    • (b) Increases by 1
    • (c) Remains the same
    • (d) Becomes zero

44. What does the binding energy per nucleon indicate about a nucleus?

    • (a) Number of protons
    • (b) Stability of the nucleus
    • (c) Decay rate
    • (d) Reaction type

45. What is the dimension of mass defect $\mathrm{\Delta }m$?

    • (a) $[\text{M}]$
    • (b) $[\text{M}\text{L}{\text{T}}^{-1}]$
    • (c) $[\text{L}{\text{T}}^{-2}]$
    • (d) $[\text{M}{\text{L}}^2{\text{T}}^{-1}]$

46. What does gamma decay emit?

    • (a) Alpha particles
    • (b) Beta particles
    • (c) High-energy photons
    • (d) Neutrons

47. What is the significance of $N=N_0{e}^{-\lambda t}$?

    • (a) Binding energy
    • (b) Radioactive decay law
    • (c) Q-value
    • (d) Nuclear reaction rate

48. What happens to the mass number $A$ in alpha decay?

    • (a) Increases by 4
    • (b) Decreases by 4
    • (c) Remains the same
    • (d) Becomes zero

49. What does carbon dating use to determine the age of a sample?

    • (a) ${}^{238}\text{U}$ decay
    • (b) ${}^{14}\text{C}$ decay
    • (c) ${}^{60}\text{Co}$ decay
    • (d) ${}^{241}\text{Am}$ decay

50. How is nuclear physics applied in spacecraft power systems?

    • (a) Increases radiation
    • (b) Uses RTGs with isotopes like ${}^{238}\text{Pu}$ for power
    • (c) Reduces stability
    • (d) Increases mass defect

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Derivation Problems

51. Derive the binding energy $E_b$ of a nucleus using the mass defect formula $E_b=\mathrm{\Delta }m{c}^2$.

52. Derive the radioactive decay law $N=N_0{e}^{-\lambda t}$.

53. Derive the Q-value of a nuclear reaction $Q=[m_{\text{reactants}}-m_{\text{products}}]c^2$.

54. Derive the half-life $T_{1/2}=\frac{\ln 2}{\lambda }$ for radioactive decay.

55. Derive the binding energy per nucleon for a given nucleus.

56. Derive the activity $A=\lambda N$ for a radioactive sample.

57. Derive the mass defect $\mathrm{\Delta }m$ for a given nucleus.

58. Derive the age of a sample using carbon dating $t=\frac{\ln (A_0/A)}{\lambda }$.

59. Derive the energy released per fission in a nuclear reactor.

60. Derive the number of nuclei $N$ after a given time $t$ for a radioactive sample.

61. Derive the Q-value for an alpha decay reaction.

62. Derive the decay constant $\lambda$ from the half-life $T_{1/2}$.

63. Derive the energy released in a fusion reaction.

64. Derive the activity $A$ after a given time $t$ for a radioactive sample.

65. Derive the number of fissions per second in a nuclear reactor given power output.

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NEET-style Conceptual Problems

66. What is the unit of the Q-value in nuclear reactions?

    • (a) MeV
    • (b) Radian
    • (c) Hertz
    • (d) Watt

67. What does the reaction ${}_9{2}^{235}\text{U}{+}_0^1\text{n}{\to }_5{6}^{141}\text{Ba}{+}_3{6}^{92}\text{Kr}+3_0^1\text{n}$ represent?

    • (a) Fusion
    • (b) Fission
    • (c) Alpha decay
    • (d) Beta decay

68. What is the relationship between $N$ and $t$ in radioactive decay?

    • (a) $N\propto t$
    • (b) $N=N_0{e}^{-\lambda t}$
    • (c) $N$ is independent of $t$
    • (d) $N\propto t^2$

69. What happens to the number of nuclei $N$ after two half-lives?

    • (a) Doubles
    • (b) Reduces to 1/4
    • (c) Remains the same
    • (d) Becomes zero

70. What is the dimension of binding energy $E_b$?

    • (a) $[\text{M}{\text{L}}^2{\text{T}}^{-2}]$
    • (b) $[\text{M}\text{L}{\text{T}}^{-1}]$
    • (c) $[\text{L}{\text{T}}^{-2}]$
    • (d) $[\text{M}{\text{L}}^2{\text{T}}^{-1}]$

71. What does the strong nuclear force do in a nucleus?

    • (a) Repels protons
    • (b) Binds nucleons together
    • (c) Emits radiation
    • (d) Increases mass defect

72. What is the role of ${}^{238}\text{Pu}$ in spacecraft power systems?

    • (a) Increases radiation
    • (b) Provides power via decay in RTGs
    • (c) Reduces stability
    • (d) Increases mass defect

73. What happens to $Z$ in ${\beta }^{+}$ decay?

    • (a) Increases by 1
    • (b) Decreases by 1
    • (c) Remains the same
    • (d) Becomes zero

74. Why does fusion release energy?

    • (a) Due to mass increase
    • (b) Due to increased binding energy per nucleon
    • (c) Due to nuclear force reduction
    • (d) Due to proton repulsion

75. What is the unit of decay constant $\lambda$ in SI units?

    • (a) s${}^{-1}$
    • (b) Joule
    • (c) Hertz
    • (d) Watt

76. What does a high binding energy per nucleon indicate?

    • (a) Low stability
    • (b) High stability
    • (c) High decay rate
    • (d) Low mass defect

77. Which decay emits an electron and an antineutrino?

    • (a) Alpha decay
    • (b) Beta minus decay
    • (c) Gamma decay
    • (d) Beta plus decay

78. What is the effect of alpha decay on a nucleus?

    • (a) Increases $Z$ by 2
    • (b) Decreases $Z$ by 2
    • (c) Increases $A$ by 4
    • (d) No change in $A$

79. What does a pseudo-force do in a non-inertial frame for nuclear calculations?

    • (a) Affects perceived decay rate
    • (b) Affects binding energy
    • (c) Creates nuclear reactions
    • (d) Reduces stability

80. What is the dimension of $\lambda N$?

    • (a) $[{\text{T}}^{-1}]$
    • (b) $[\text{M}\text{L}{\text{T}}^{-1}]$
    • (c) $[\text{L}{\text{T}}^{-2}]$
    • (d) $[\text{M}{\text{L}}^2{\text{T}}^{-1}]$

81. What is the role of ${}^{60}\text{Co}$ in medical applications?

    • (a) Carbon dating
    • (b) Radiation therapy via gamma rays
    • (c) Smoke detection
    • (d) Nuclear power

82. What happens to the energy released in fission?

    • (a) Decreases due to mass defect
    • (b) Increases due to higher binding energy per nucleon in products
    • (c) Remains the same
    • (d) Becomes zero

83. Why are heavy nuclei used in fission reactions?

    • (a) Due to high stability
    • (b) Due to lower binding energy per nucleon
    • (c) Due to high mass defect
    • (d) Due to low decay rate

84. What is the significance of $931.494\text{MeV/u}$?

    • (a) Decay constant
    • (b) Energy equivalent of 1 u mass defect
    • (c) Q-value
    • (d) Half-life

85. What is the unit of half-life $T_{1/2}$?

    • (a) Second
    • (b) Joule
    • (c) Hertz
    • (d) Watt

86. What does a low Q-value in a nuclear reaction indicate?

    • (a) High energy release
    • (b) Low energy release or absorption
    • (c) No energy change
    • (d) High stability

87. What is the physical significance of $\mathrm{\Delta }m{c}^2$?

    • (a) Mass defect
    • (b) Energy released or absorbed in a reaction
    • (c) Decay constant
    • (d) Half-life

88. Why is ${}_2{6}^{56}\text{Fe}$ the most stable nucleus?

    • (a) Due to low binding energy
    • (b) Due to highest binding energy per nucleon
    • (c) Due to high decay rate
    • (d) Due to low mass defect

89. What is the dimension of $e^{-\lambda t}$?

    • (a) Dimensionless
    • (b) $[\text{M}\text{L}{\text{T}}^{-1}]$
    • (c) $[\text{L}{\text{T}}^{-2}]$
    • (d) $[\text{M}{\text{L}}^2{\text{T}}^{-1}]$

90. How does nuclear physics contribute to medical imaging?

    • (a) Via nuclear reactors
    • (b) Via radioactive tracers like ${}^{99m}\text{Tc}$
    • (c) Via smoke detectors
    • (d) Via carbon dating

91. What is the role of neutrons in fission?

    • (a) Decrease $Z$
    • (b) Trigger chain reactions
    • (c) Increase stability
    • (d) Emit gamma rays

92. What does a bright line in an emission spectrum indicate?

    • (a) Electron absorption
    • (b) Electron emission
    • (c) Nuclear decay
    • (d) Continuous energy

93. What is the physical significance of $\frac{\ln 2}{\lambda }$?

    • (a) Binding energy
    • (b) Half-life of a radioactive sample
    • (c) Q-value
    • (d) Mass defect

94. What is the dimension of $c^2$ in $E=\mathrm{\Delta }m{c}^2$?

    • (a) $[{\text{L}}^2{\text{T}}^{-2}]$
    • (b) $[\text{M}\text{L}{\text{T}}^{-1}]$
    • (c) $[\text{L}{\text{T}}^{-2}]$
    • (d) $[\text{M}{\text{L}}^2{\text{T}}^{-1}]$

95. Why does fission produce neutrons?

    • (a) To increase $Z$
    • (b) To sustain chain reactions
    • (c) To emit gamma rays
    • (d) To reduce mass defect

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NEET-style Numerical Problems

96. Calculate the binding energy per nucleon of ${}_2^4\text{He}$ in MeV (use mass defect from Problem 1).

    • (a) 7.06 MeV
    • (b) 7.07 MeV
    • (c) 7.08 MeV
    • (d) 7.09 MeV

97. A radioactive sample has $T_{1/2}=5\text{years}$, initial activity 400 Bq. Calculate activity after 10 years in Bq.

    • (a) 99 Bq
    • (b) 100 Bq
    • (c) 101 Bq
    • (d) 102 Bq

98. Calculate the Q-value of ${}_1^3\text{H}{+}_1^3\text{H}{\to }_2^4\text{He}+2_0^1\text{n}$ in MeV. Given: $m{(}_1^3\text{H})=3.0160\text{u}$, $m{(}_2^4\text{He})=4.0026\text{u}$, $m{(}_0^1\text{n})=1.0087\text{u}$.

    • (a) 11.30 MeV
    • (b) 11.31 MeV
    • (c) 11.32 MeV
    • (d) 11.33 MeV

99. A sample has $\lambda =0.004{\text{s}}^{-1}$, $N_0={10}^9$. Calculate $N$ after 250 s.

    • (a) $3.67\times {10}^8$
    • (b) $3.68\times {10}^8$
    • (c) $3.69\times {10}^8$
    • (d) $3.70\times {10}^8$

100. A nuclear reactor produces 5 MW. If each fission releases 200 MeV, calculate fissions per second.
     - (a) $1.56\times {10}^{17}$
     - (b) $1.57\times {10}^{17}$
     - (c) $1.58\times {10}^{17}$
     - (d) $1.59\times {10}^{17}$

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