Energy from the Nucleus Problems

This section provides 100 problems to test your understanding of nuclear energy, including calculations of energy release in fission and fusion, nuclear reactor dynamics (e.g., fission rates, criticality), applications like RTGs and nuclear propulsion in spacecraft, and challenges such as radioactive waste decay. 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 energy, a key topic for JEE/NEET success.

Numerical Problems

1. Calculate the Q-value of the fission reaction ${}_9{2}^{235}\text{U}{+}_0^1\text{n}{\to }_5{6}^{141}\text{Ba}{+}_3{6}^{92}\text{Kr}+3_0^1\text{n}$ in MeV. Given: $m{(}_9{2}^{235}\text{U})=235.0439\text{u}$, $m{(}_0^1\text{n})=1.0087\text{u}$, $m{(}_5{6}^{141}\text{Ba})=140.9144\text{u}$, $m{(}_3{6}^{92}\text{Kr})=91.9262\text{u}$, $c^2=931.494\text{MeV/u}$.

   • (a) 173.2 MeV
   • (b) 173.3 MeV
   • (c) 173.4 MeV
   • (d) 173.5 MeV

2. A nuclear reactor produces 2000 MW of thermal power. If each fission releases 200 MeV, calculate the number of fissions per second.

   • (a) $6.24\times {10}^{19}$
   • (b) $6.25\times {10}^{19}$
   • (c) $6.26\times {10}^{19}$
   • (d) $6.27\times {10}^{19}$

3. Calculate the Q-value of the fusion 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) 17.58 MeV
   • (b) 17.59 MeV
   • (c) 17.60 MeV
   • (d) 17.61 MeV

4. An RTG using ${}^{238}\text{Pu}$ ($T_{1/2}=87.7\text{years}$) has an activity of 1000 Ci, with each decay releasing 5.5 MeV. Calculate the power output in Watts.

   • (a) 32.54 W
   • (b) 32.55 W
   • (c) 32.56 W
   • (d) 32.57 W

5. A nuclear power plant produces 1200 MW of electrical power at 40% efficiency. Calculate the thermal power in MW.

   • (a) 2999 MW
   • (b) 3000 MW
   • (c) 3001 MW
   • (d) 3002 MW

6. High-level nuclear waste contains ${}^{137}\text{Cs}$ ($T_{1/2}=30.17\text{years}$) with an initial activity of 800 Ci. Calculate the time (in years) for the activity to reduce to 1 Ci.

   • (a) 299 years
   • (b) 300 years
   • (c) 301 years
   • (d) 302 years

7. A spacecraft nuclear thermal propulsion (NTP) system produces 150 MW of thermal power, using ${}^{235}\text{U}$ with each fission releasing 200 MeV. Calculate the fission rate in fissions per second.

   • (a) $4.68\times {10}^{18}$
   • (b) $4.69\times {10}^{18}$
   • (c) $4.70\times {10}^{18}$
   • (d) $4.71\times {10}^{18}$

8. Calculate the Q-value of the fusion reaction ${}_1^2\text{H}{+}_1^2\text{H}{\to }_2^3\text{He}{+}_0^1\text{n}$ 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

9. A nuclear plant produces 500 MW electrical power at 35% efficiency. Calculate the mass of ${}^{235}\text{U}$ consumed per day (in kg), assuming 200 MeV per fission. Given: molar mass of ${}^{235}\text{U}=235\text{g/mol}$.

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

10. An RTG with ${}^{238}\text{Pu}$ ($T_{1/2}=87.7\text{years}$) has an initial activity of 200 Ci. Calculate the activity after 100 years in Ci.

    • (a) 61.5 Ci
    • (b) 61.6 Ci
    • (c) 61.7 Ci
    • (d) 61.8 Ci

11. A reactor produces 4000 MW thermal power. If each fission releases 200 MeV, calculate the mass of ${}^{235}\text{U}$ consumed per day (in kg).

    • (a) 1.92 kg
    • (b) 1.93 kg
    • (c) 1.94 kg
    • (d) 1.95 kg

12. High-level waste with ${}^{90}\text{Sr}$ ($T_{1/2}=28.8\text{years}$) has an initial activity of 600 Ci. Calculate the activity after 50 years in Ci.

    • (a) 149 Ci
    • (b) 150 Ci
    • (c) 151 Ci
    • (d) 152 Ci

13. A fusion reactor produces 1 GW using the D-T reaction ($Q=17.6\text{MeV}$). Calculate the fusion rate in fusions per second.

    • (a) $3.54\times {10}^{20}$
    • (b) $3.55\times {10}^{20}$
    • (c) $3.56\times {10}^{20}$
    • (d) $3.57\times {10}^{20}$

14. A nuclear plant produces 800 MW electrical power at 32% efficiency. Calculate the thermal power in MW.

    • (a) 2499 MW
    • (b) 2500 MW
    • (c) 2501 MW
    • (d) 2502 MW

15. An RTG with ${}^{238}\text{Pu}$ ($T_{1/2}=87.7\text{years}$) produces 50 W initially, with each decay releasing 5.5 MeV. Calculate the initial activity in Ci.

    • (a) 356 Ci
    • (b) 357 Ci
    • (c) 358 Ci
    • (d) 359 Ci

16. A reactor with a fission rate of $5\times {10}^{19}$ fissions/s releases 200 MeV per fission. Calculate the thermal power in MW.

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

17. High-level waste with ${}^{137}\text{Cs}$ ($T_{1/2}=30.17\text{years}$) has an initial activity of 1000 Ci. Calculate the time (in years) for activity to reduce to 10 Ci.

    • (a) 229 years
    • (b) 230 years
    • (c) 231 years
    • (d) 232 years

18. A spacecraft NTP system produces 200 MW, heating hydrogen at 1 kg/s, $T=2800\text{K}$, $\gamma =1.4$, molar mass $M=2\text{g/mol}$. Calculate exhaust velocity in m/s ($R=8.314\text{J/mol·K}$).

    • (a) 8099 m/s
    • (b) 8100 m/s
    • (c) 8101 m/s
    • (d) 8102 m/s

19. A fusion reactor produces 500 MW using D-T fusion ($Q=17.6\text{MeV}$). Calculate the mass of deuterium consumed per day (in kg), molar mass $M=2\text{g/mol}$.

    • (a) 0.122 kg
    • (b) 0.123 kg
    • (c) 0.124 kg
    • (d) 0.125 kg

20. A reactor produces 3000 MW thermal power. If each fission releases 200 MeV, calculate the mass of ${}^{235}\text{U}$ consumed per day (in kg).

    • (a) 1.44 kg
    • (b) 1.45 kg
    • (c) 1.46 kg
    • (d) 1.47 kg

21. High-level waste with ${}^{90}\text{Sr}$ ($T_{1/2}=28.8\text{years}$) has an initial activity of 400 Ci. Calculate the activity after 100 years in Ci.

    • (a) 36.0 Ci
    • (b) 36.1 Ci
    • (c) 36.2 Ci
    • (d) 36.3 Ci

22. An RTG with ${}^{238}\text{Pu}$ ($T_{1/2}=87.7\text{years}$) produces 20 W, with each decay releasing 5.5 MeV. Calculate the initial activity in Ci.

    • (a) 142 Ci
    • (b) 143 Ci
    • (c) 144 Ci
    • (d) 145 Ci

23. A nuclear plant produces 1500 MW electrical power at 38% efficiency. Calculate the thermal power in MW.

    • (a) 3946 MW
    • (b) 3947 MW
    • (c) 3948 MW
    • (d) 3949 MW

24. A reactor with a fission rate of $2\times {10}^{20}$ fissions/s releases 200 MeV per fission. Calculate the thermal power in MW.

    • (a) 6399 MW
    • (b) 6400 MW
    • (c) 6401 MW
    • (d) 6402 MW

25. A fusion reactor produces 2 GW using D-T fusion ($Q=17.6\text{MeV}$). Calculate the fusion rate in fusions per second.

    • (a) $7.09\times {10}^{20}$
    • (b) $7.10\times {10}^{20}$
    • (c) $7.11\times {10}^{20}$
    • (d) $7.12\times {10}^{20}$

26. High-level waste with ${}^{137}\text{Cs}$ ($T_{1/2}=30.17\text{years}$) has an initial activity of 500 Ci. Calculate the activity after 200 years in Ci.

    • (a) 4.54 Ci
    • (b) 4.55 Ci
    • (c) 4.56 Ci
    • (d) 4.57 Ci

27. A spacecraft NTP system produces 300 MW, heating hydrogen at 1.5 kg/s, $T=3000\text{K}$, $\gamma =1.4$, $M=2\text{g/mol}$. Calculate exhaust velocity in m/s.

    • (a) 8348 m/s
    • (b) 8349 m/s
    • (c) 8350 m/s
    • (d) 8351 m/s

28. A reactor produces 2500 MW thermal power. Calculate the mass of ${}^{235}\text{U}$ consumed per day (in kg) if each fission releases 200 MeV.

    • (a) 1.20 kg
    • (b) 1.21 kg
    • (c) 1.22 kg
    • (d) 1.23 kg

29. An RTG with ${}^{238}\text{Pu}$ ($T_{1/2}=87.7\text{years}$) has an initial activity of 300 Ci. Calculate the activity after 50 years in Ci.

    • (a) 168 Ci
    • (b) 169 Ci
    • (c) 170 Ci
    • (d) 171 Ci

30. A nuclear plant produces 600 MW electrical power at 30% efficiency. Calculate the thermal power in MW.

    • (a) 1999 MW
    • (b) 2000 MW
    • (c) 2001 MW
    • (d) 2002 MW

31. A spacecraft fusion engine produces 1 GW, $Q=17.6\text{MeV}$. Calculate the mass of deuterium consumed per day (in kg), $M=2\text{g/mol}$.

    • (a) 0.244 kg
    • (b) 0.245 kg
    • (c) 0.246 kg
    • (d) 0.247 kg

32. High-level waste with ${}^{90}\text{Sr}$ ($T_{1/2}=28.8\text{years}$) has an initial activity of 1000 Ci. Calculate the time (in years) to reduce to 1 Ci.

    • (a) 191 years
    • (b) 192 years
    • (c) 193 years
    • (d) 194 years

33. A reactor with a fission rate of $1\times {10}^{20}$ fissions/s releases 200 MeV per fission. Calculate the thermal power in MW.

    • (a) 3199 MW
    • (b) 3200 MW
    • (c) 3201 MW
    • (d) 3202 MW

34. A nuclear plant produces 1800 MW electrical power at 36% efficiency. Calculate the thermal power in MW.

    • (a) 4999 MW
    • (b) 5000 MW
    • (c) 5001 MW
    • (d) 5002 MW

35. An RTG with ${}^{238}\text{Pu}$ ($T_{1/2}=87.7\text{years}$) has an initial activity of 150 Ci. Calculate the activity after 150 years in Ci.

    • (a) 29.9 Ci
    • (b) 30.0 Ci
    • (c) 30.1 Ci
    • (d) 30.2 Ci

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Conceptual Problems

36. What is the primary source of energy in nuclear fission?

    • (a) Kinetic energy of neutrons
    • (b) Increase in binding energy per nucleon in products
    • (c) Decrease in mass number
    • (d) Increase in atomic number

37. What is the role of control rods in a nuclear reactor?

    • (a) Slow neutrons
    • (b) Absorb neutrons to regulate reaction rate
    • (c) Cool the reactor
    • (d) Fuel the reactor

38. What is the unit of power output in a nuclear reactor in SI units?

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

39. What happens to the reaction rate in a nuclear reactor if the multiplication factor $k>1$?

    • (a) Decreases
    • (b) Increases exponentially
    • (c) Remains constant
    • (d) Becomes zero

40. What type of reaction powers the Sun?

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

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

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

42. What does a high specific impulse in NTP indicate?

    • (a) Low efficiency
    • (b) High efficiency for propulsion
    • (c) High mass consumption
    • (d) Low thrust

43. What happens to nuclear waste activity over time?

    • (a) Increases exponentially
    • (b) Decreases exponentially
    • (c) Remains constant
    • (d) Becomes zero instantly

44. What is a major challenge of nuclear energy?

    • (a) High CO${}_2$ emissions
    • (b) Radioactive waste management
    • (c) Low energy output
    • (d) Fuel abundance

45. What is the dimension of $Q=\mathrm{\Delta }m{c}^2$?

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

46. What does the moderator do in a nuclear reactor?

    • (a) Absorbs neutrons
    • (b) Slows neutrons to thermal energies
    • (c) Increases reaction rate
    • (d) Cools the reactor

47. What is the significance of $k=1$ in a nuclear reactor?

    • (a) Critical state, steady reaction
    • (b) Supercritical state
    • (c) Subcritical state
    • (d) Shutdown state

48. What happens to the efficiency of a nuclear power plant?

    • (a) 100% due to high energy release
    • (b) ~33–40% due to thermodynamic limits
    • (c) 0% due to energy loss
    • (d) Varies randomly

49. What does an RTG use to produce power?

    • (a) Fission reactions
    • (b) Fusion reactions
    • (c) Decay heat from isotopes like ${}^{238}\text{Pu}$
    • (d) Chemical reactions

50. How does nuclear energy contribute to spacecraft propulsion?

    • (a) Increases mass
    • (b) Enables NTP and RTGs for efficient power and thrust
    • (c) Reduces efficiency
    • (d) Increases CO${}_2$ emissions

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Derivation Problems

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

52. Derive the fission rate in a nuclear reactor given its thermal power output.

53. Derive the power output of an RTG given its activity and energy per decay.

54. Derive the time for nuclear waste to decay to a specific activity level.

55. Derive the thermal power in a nuclear reactor given the fission rate.

56. Derive the exhaust velocity in an NTP system $v_e\approx \sqrt{\frac{\gamma RT}{M}}$.

57. Derive the mass of fuel consumed in a reactor given its power output.

58. Derive the activity $A$ of nuclear waste after a given time $t$.

59. Derive the fusion rate in a reactor given its power output.

60. Derive the thermal power of a nuclear plant given its electrical power and efficiency.

61. Derive the Q-value for a fusion reaction.

62. Derive the mass of deuterium consumed in a fusion reactor.

63. Derive the time for an RTG's activity to decrease to a specific level.

64. Derive the fission rate in an NTP system given its power output.

65. Derive the efficiency $\eta$ of a nuclear power plant given electrical and thermal power.

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NEET-style Conceptual Problems

66. What is the unit of energy release $Q$ 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 thermal power and electrical power in a nuclear plant?

    • (a) ${\text{Power}}_{\text{thermal}}={\text{Power}}_{\text{electrical}}$
    • (b) ${\text{Power}}_{\text{thermal}}={\text{Power}}_{\text{electrical}}/\eta$
    • (c) ${\text{Power}}_{\text{thermal}}$ is independent
    • (d) ${\text{Power}}_{\text{thermal}}\propto {\text{Power}}_{\text{electrical}}^2$

69. What happens to the activity of nuclear waste after one half-life?

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

70. What is the dimension of power output in a nuclear reactor?

    • (a) $[\text{M}{\text{L}}^2{\text{T}}^{-3}]$
    • (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 coolant do in a nuclear reactor?

    • (a) Slows neutrons
    • (b) Transfers heat to produce steam
    • (c) Absorbs neutrons
    • (d) Fuels the reactor

72. What is the role of nuclear energy in spacecraft?

    • (a) Increases CO${}_2$ emissions
    • (b) Powers systems via RTGs and NTP
    • (c) Reduces efficiency
    • (d) Increases mass defect

73. What happens to the reaction rate in a reactor if $k<1$?

    • (a) Increases exponentially
    • (b) Decreases and stops
    • (c) Remains constant
    • (d) Becomes infinite

74. Why does fusion require high temperatures?

    • (a) To increase mass defect
    • (b) To overcome Coulomb repulsion between nuclei
    • (c) To reduce binding energy
    • (d) To decrease reaction rate

75. What is the unit of activity in nuclear waste decay?

    • (a) Curie (Ci)
    • (b) Joule
    • (c) Hertz
    • (d) Watt

76. What does a high exhaust velocity in NTP indicate?

    • (a) Low efficiency
    • (b) High specific impulse
    • (c) High mass consumption
    • (d) Low power output

77. Which process produces less radioactive waste?

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

78. What is the effect of a nuclear accident like Fukushima?

    • (a) Increases CO${}_2$ emissions
    • (b) Radioactive contamination
    • (c) Increases efficiency
    • (d) Reduces waste

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

    • (a) Affects perceived reaction rate
    • (b) Affects Q-value
    • (c) Creates fusion
    • (d) Reduces efficiency

80. What is the dimension of $\sqrt{\frac{\gamma RT}{M}}$?

    • (a) $[\text{L}{\text{T}}^{-1}]$
    • (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 nuclear energy in desalination?

    • (a) Increases CO${}_2$ emissions
    • (b) Provides heat for water purification
    • (c) Reduces efficiency
    • (d) Increases waste

82. What happens to the energy release in fusion?

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

83. Why are advanced reactors (Gen IV) being developed?

    • (a) To increase CO${}_2$ emissions
    • (b) To improve efficiency and reduce waste
    • (c) To decrease safety
    • (d) To increase proliferation

84. What is the significance of $17.6\text{MeV}$ in the D-T fusion reaction?

    • (a) Decay constant
    • (b) Q-value of the reaction
    • (c) Mass defect
    • (d) Half-life

85. What is the unit of exhaust velocity $v_e$ in NTP?

    • (a) m/s
    • (b) Joule
    • (c) Hertz
    • (d) Watt

86. What does a high $k$ value in a reactor indicate?

    • (a) Stable operation
    • (b) Potential for uncontrolled reaction
    • (c) Shutdown state
    • (d) Low efficiency

87. What is the physical significance of $e^{-\lambda t}$ in waste decay?

    • (a) Q-value
    • (b) Exponential decrease in activity
    • (c) Mass defect
    • (d) Fission rate

88. Why is nuclear energy considered low-carbon?

    • (a) Due to high CO${}_2$ emissions
    • (b) Due to minimal greenhouse gas emissions
    • (c) Due to high waste production
    • (d) Due to low efficiency

89. What is the dimension of $A\times Q$ in RTG power calculation?

    • (a) $[\text{M}{\text{L}}^2{\text{T}}^{-3}]$
    • (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 fusion energy aim to impact future energy production?

    • (a) Increases waste
    • (b) Provides a clean, limitless energy source
    • (c) Reduces safety
    • (d) Increases CO${}_2$ emissions

91. What is the role of thermocouples in an RTG?

    • (a) Increase decay rate
    • (b) Convert heat to electricity
    • (c) Absorb neutrons
    • (d) Cool the system

92. What does a low efficiency in nuclear plants indicate?

    • (a) High thermal power
    • (b) Thermodynamic limitations
    • (c) High electrical power
    • (d) No energy loss

93. What is the physical significance of $\frac{\text{Power}}{Q}$?

    • (a) Mass defect
    • (b) Reaction rate in a reactor
    • (c) Decay constant
    • (d) Efficiency

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

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

95. Why are nuclear plants efficient for large-scale energy?

    • (a) Due to high CO${}_2$ emissions
    • (b) Due to high energy density of nuclear fuel
    • (c) Due to low output
    • (d) Due to high waste

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NEET-style Numerical Problems

96. Calculate the Q-value of ${}_9{2}^{235}\text{U}{+}_0^1\text{n}{\to }_5{4}^{139}\text{Xe}{+}_3{8}^{95}\text{Sr}+2_0^1\text{n}$ in MeV. Given: $m{(}_9{2}^{235}\text{U})=235.0439\text{u}$, $m{(}_0^1\text{n})=1.0087\text{u}$, $m{(}_5{4}^{139}\text{Xe})=138.9188\text{u}$, $m{(}_3{8}^{95}\text{Sr})=94.9194\text{u}$.

    • (a) 185.1 MeV
    • (b) 185.2 MeV
    • (c) 185.3 MeV
    • (d) 185.4 MeV

97. A nuclear reactor produces 1000 MW thermal power. If each fission releases 200 MeV, calculate the fission rate in fissions per second.

    • (a) $3.12\times {10}^{19}$
    • (b) $3.13\times {10}^{19}$
    • (c) $3.14\times {10}^{19}$
    • (d) $3.15\times {10}^{19}$

98. An RTG with ${}^{238}\text{Pu}$ ($T_{1/2}=87.7\text{years}$) has an initial activity of 400 Ci. Calculate the activity after 100 years in Ci.

    • (a) 123.2 Ci
    • (b) 123.3 Ci
    • (c) 123.4 Ci
    • (d) 123.5 Ci

99. A nuclear plant produces 900 MW electrical power at 34% efficiency. Calculate the thermal power in MW.

    • (a) 2646 MW
    • (b) 2647 MW
    • (c) 2648 MW
    • (d) 2649 MW

100. A spacecraft NTP system produces 250 MW, heating hydrogen at 2 kg/s, $T=2900\text{K}$, $\gamma =1.4$, $M=2\text{g/mol}$. Calculate exhaust velocity in m/s.
     - (a) 8224 m/s
     - (b) 8225 m/s
     - (c) 8226 m/s
     - (d) 8227 m/s

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