IB Physics Quiz: Apply Fission
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Apply FissionQuestion 1 of 20

In a specific fission reaction, a neutron is absorbed by a Uranium-235 nucleus. The products are a Xenon-140 nucleus, a Strontium-94 nucleus, and two additional neutrons. Relevant masses: Uranium-235: 235.0439 u Neutron: 1.0087 u Xenon-140: 139.9216 u Strontium-94: 93.9154 u (1 u = 931.5 MeV c⁻²)

What is the approximate energy released in this specific fission reaction?

165 MeV
185 MeV
205 MeV
2.20 × 10⁵ MeV
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IB Physics Quiz

IB Physics Quiz: Apply Fission

Practice Apply Fission in IB Physics with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

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This quiz focuses on Apply Fission, giving you a quick way to practice the rules, question types, and explanations that matter most for IB Physics.

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Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

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Question 1

In a specific fission reaction, a neutron is absorbed by a Uranium-235 nucleus. The products are a Xenon-140 nucleus, a Strontium-94 nucleus, and two additional neutrons. Relevant masses: Uranium-235: 235.0439 u Neutron: 1.0087 u Xenon-140: 139.9216 u Strontium-94: 93.9154 u (1 u = 931.5 MeV c⁻²)

What is the approximate energy released in this specific fission reaction?

  1. 165 MeV
  2. 185 MeV (correct answer)
  3. 205 MeV
  4. 2.20 × 10⁵ MeV
Explanation: First, calculate the total mass of the reactants: Mass_reactants = m(U-235) + m(neutron) = 235.0439 u + 1.0087 u = 236.0526 u. Next, calculate the total mass of the products: Mass_products = m(Xe-140) + m(Sr-94) + 2 × m(neutron) = 139.9216 u + 93.9154 u + 2 × (1.0087 u) = 235.8544 u. The mass defect (Δm) is the difference: Δm = 236.0526 u - 235.8544 u = 0.1982 u. Finally, convert the mass defect to energy: E = Δm × 931.5 MeV/u = 0.1982 u × 931.5 MeV/u ≈ 184.6 MeV.

Question 2

A nuclear reactor generates 108 MW of thermal power. What is the approximate rate at which mass is converted to energy in the reactor?

  1. 1.2 g s⁻¹
  2. 1.2 mg s⁻¹
  3. 1.2 kg s⁻¹
  4. 1.2 μg s⁻¹ (correct answer)
Explanation: The rate at which mass is converted to energy can be found using Einstein's mass-energy relation E = mc². The rate of mass conversion is Δm/Δt = P/c², where P is the thermal power. Δm/Δt = (1.08 × 10⁸ J/s) / (3.00 × 10⁸ m/s)² = 1.2 × 10⁻⁹ kg/s. Converting to micrograms: (1.2 × 10⁻⁹ kg/s) × (10⁹ μg/kg) = 1.2 μg/s.

Question 3

Following a fission event, neutrons are emitted. Most are emitted 'promptly' (within ~10⁻¹⁴ s), but a small fraction (~0.65%) are 'delayed', emitted seconds later from decaying fission products. What is the crucial role of these delayed neutrons in a nuclear reactor?

  1. They provide the majority of the energy released during fission.
  2. They are much slower than prompt neutrons, making them easier to moderate.
  3. They significantly slow down the timescale of the chain reaction, allowing it to be mechanically controlled. (correct answer)
  4. They cause fission in U-238, which increases the overall power output of the reactor.
Explanation: If the chain reaction depended only on prompt neutrons, the power level would change almost instantaneously, far too quickly for mechanical systems like control rods to respond. The presence of delayed neutrons extends the average time between neutron generations from microseconds to tenths of a second. This slowing of the reaction dynamics is what makes a nuclear reactor controllable.

Question 4

In some reactor designs, if the temperature of the moderator increases, its density decreases. This leads to less effective neutron moderation and a reduction in the fission rate. This phenomenon is known as a...

  1. positive temperature coefficient of reactivity.
  2. neutron poisoning effect.
  3. Doppler broadening effect.
  4. negative temperature coefficient of reactivity. (correct answer)
Explanation: The temperature coefficient of reactivity describes how the reactor's reactivity (its tendency to sustain a chain reaction) changes with temperature. If an increase in temperature causes a decrease in reactivity (and thus a decrease in the fission rate), it is a negative feedback loop. This is a desirable safety feature. Therefore, it is called a negative temperature coefficient of reactivity.

Question 5

The fission of a single Uranium-235 nucleus releases approximately 200 MeV of energy. A nuclear power plant has a continuous electrical power output of 500 MW. If the plant's overall efficiency is 32%, approximately how many Uranium-235 fissions occur per second? (1 MeV = 1.6 × 10⁻¹³ J)

  1. 1.6 × 10¹⁹
  2. 4.9 × 10¹⁹ (correct answer)
  3. 9.8 × 10¹⁸
  4. 1.6 × 10²⁰
Explanation: First, calculate the required thermal power from the reactor. Thermal Power = Electrical Power / Efficiency = (500 × 10⁶ W) / 0.32 = 1.5625 × 10⁹ W. Next, convert the energy per fission to Joules: Energy = 200 MeV × (1.6 × 10⁻¹³ J/MeV) = 3.2 × 10⁻¹¹ J. Finally, the number of fissions per second is the total thermal power divided by the energy per fission: Rate = (1.5625 × 10⁹ J/s) / (3.2 × 10⁻¹¹ J/fission) ≈ 4.9 × 10¹⁹ fissions/s.

Question 6

In a pressurized water reactor, the thermal utilization factor f represents the fraction of thermal neutrons absorbed in the fuel. If f = 0.85, and the reactor contains fuel rods with 3.2% enriched uranium in a water moderator, what does the remaining 0.15 fraction primarily represent?

  1. Neutrons absorbed by control rods and structural materials only
  2. Neutrons absorbed by 238^{238}U in the fuel rods only
  3. Neutrons absorbed by water moderator, control rods, and structural materials (correct answer)
  4. Neutrons that leak out of the reactor core entirely
Explanation: The thermal utilization factor f accounts for thermal neutrons absorbed in fissile material versus all other materials in the reactor core. The remaining fraction (1-f) = 0.15 represents thermal neutrons absorbed by the water moderator, control rods, structural materials, and other non-fissile components. Choice A ignores moderator absorption. Choice B incorrectly includes 238^{238}U, which primarily absorbs fast neutrons. Choice D confuses absorption with leakage, which is accounted for separately in reactor physics.

Question 7

A nuclear power plant's reactor core contains fuel assemblies arranged in a critical configuration. If the geometric buckling B2B^2 is 8.5×10−4 cm−28.5 × 10^{-4} \text{ cm}^{-2} and the material buckling Bm2B_m^2 is 9.2×10−4 cm−29.2 × 10^{-4} \text{ cm}^{-2}, what modification would bring the reactor closer to the critical condition?

  1. Increase fuel enrichment to raise the material buckling value
  2. Insert control rods partially to reduce the geometric buckling
  3. Add neutron reflectors around the core to reduce neutron leakage (correct answer)
  4. Increase moderator temperature to enhance neutron absorption
Explanation: For criticality, geometric buckling must equal material buckling (B2=Bm2B^2 = B_m^2). Currently B2<Bm2B^2 < B_m^2, indicating the reactor is subcritical due to excessive neutron leakage. Adding reflectors reduces leakage, effectively increasing the geometric buckling toward the material buckling value. Choice A would increase Bm2B_m^2 further from B2B^2. Choice B would decrease B2B^2 further. Choice D would decrease reactivity through increased neutron absorption.

Question 8

In uranium enrichment, the mass difference between 235^{235}UF₆ and 238^{238}UF₆ molecules affects separation efficiency. Given that fluorine has atomic mass 19.0 u, uranium-235 has mass 235.0 u, and uranium-238 has mass 238.0 u, what is the percentage mass difference between these two uranium hexafluoride molecules?

  1. 0.85% mass difference between UF₆ isotopomers (correct answer)
  2. 0.64% mass difference between UF₆ isotopomers
  3. 1.28% mass difference between UF₆ isotopomers
  4. 1.67% mass difference between UF₆ isotopomers
Explanation: When you encounter uranium enrichment problems, you're dealing with isotope separation based on mass differences. The key insight is that even small mass differences between isotopomers (molecules containing different isotopes) can be exploited for separation. To find the percentage mass difference, you need to calculate the total molecular masses first. For 235^{235}UF₆: one uranium-235 atom (235.0 u) plus six fluorine atoms (6 × 19.0 u = 114.0 u) gives 349.0 u total. For 238^{238}UF₆: one uranium-238 atom (238.0 u) plus six fluorine atoms (114.0 u) gives 352.0 u total. The mass difference is 352.0 - 349.0 = 3.0 u. The percentage difference is calculated as: 3.0352.0×100%=0.85%\frac{3.0}{352.0} × 100\% = 0.85\% Looking at the wrong answers: Choice B (0.64%) likely comes from using the wrong denominator or making an arithmetic error. Choice C (1.28%) might result from incorrectly doubling some factor or using the uranium mass difference alone without accounting for the full molecule. Choice D (1.67%) could come from using the lighter isotopomer's mass as the denominator instead of the heavier one. The correct answer is A (0.85%). Remember that in isotope separation problems, always calculate the full molecular mass including all atoms, not just the isotopic component. The small percentage differences explain why uranium enrichment requires sophisticated techniques like gas diffusion or centrifugation to achieve meaningful separation.

Question 9

A fast neutron with kinetic energy 2.0 MeV collides elastically with a stationary hydrogen nucleus in a moderator. After the collision, the neutron continues in the same direction but with reduced speed. What is the maximum fraction of its initial kinetic energy that the neutron can lose in this single collision?

  1. 0.25 (25% energy loss)
  2. 0.50 (50% energy loss)
  3. 0.75 (75% energy loss)
  4. 1.0 (100% energy loss) (correct answer)
Explanation: In an elastic collision between equal masses where one is initially at rest, maximum energy transfer occurs in a head-on collision. For a neutron (mass ≈ proton mass) colliding with a hydrogen nucleus (proton), the neutron can transfer all its kinetic energy to the proton and come to rest. The energy transfer fraction is 4m1m2(m1+m2)2\frac{4m_1m_2}{(m_1+m_2)^2}, which equals 1 when m1=m2m_1 = m_2. Choice A applies the formula for a deuteron target. Choice B assumes average energy loss. Choice C uses incorrect collision dynamics.

Question 10

In a nuclear reactor, the reproduction factor k is defined as the ratio of neutrons produced in one generation to neutrons absorbed in the previous generation. If a reactor has an initial neutron population of 101210^{12} neutrons and k = 1.003, approximately how many generations will it take for the neutron population to double?

  1. 150 generations
  2. 230 generations (correct answer)
  3. 330 generations
  4. 450 generations
Explanation: The neutron population grows as N(t)=N0ktN(t) = N_0 k^t where t is the number of generations. For doubling: 2N0=N0kt2N_0 = N_0 k^t, so 2=(1.003)t2 = (1.003)^t. Taking natural log: ln⁡(2)=tln⁡(1.003)\ln(2) = t \ln(1.003). Therefore t=ln⁡(2)ln⁡(1.003)=0.6930.002996≈231t = \frac{\ln(2)}{\ln(1.003)} = \frac{0.693}{0.002996} ≈ 231 generations. Choice A uses k−1k-1 instead of ln⁡(k)\ln(k). Choice C incorrectly uses log⁡10\log_{10}. Choice D uses the wrong formula entirely.

Question 11

A research reactor uses 235^{235}U fuel with a thermal fission cross-section of 585 barns and a thermal absorption cross-section of 694 barns. If the average number of neutrons produced per thermal fission is 2.42, what is the reproduction factor η (eta) for this fuel?

  1. 1.89
  2. 2.04 (correct answer)
  3. 2.42
  4. 2.56
Explanation: The reproduction factor η is defined as η = ν × (σ_f/σ_a), where ν is the average number of neutrons per fission, σ_f is the fission cross-section, and σ_a is the absorption cross-section. Therefore: η = 2.42 × (585/694) = 2.42 × 0.843 = 2.04. Choice A uses the wrong ratio (σ_a/σ_f). Choice C incorrectly assumes all absorptions lead to fission. Choice D adds the cross-sections instead of taking their ratio.

Question 12

In a fast breeder reactor, 238^{238}U captures neutrons to eventually produce 239^{239}Pu through beta decay processes. If the reactor has a breeding ratio of 1.15, and consumes 800 kg of fissile material per year, how much new fissile material is produced annually?

  1. 920 kg of new fissile material per year (correct answer)
  2. 680 kg of new fissile material per year
  3. 1150 kg of new fissile material per year
  4. 1380 kg of new fissile material per year
Explanation: Nuclear reactor physics involves understanding how breeding ratios quantify a reactor's ability to produce new fissile material. The breeding ratio tells you how much new fissile material is created relative to what's consumed - it's a fundamental measure of reactor efficiency. A breeding ratio of 1.15 means that for every unit of fissile material consumed, 1.15 units of new fissile material are produced. This is straightforward multiplication: if 800 kg of fissile material is consumed annually, then the reactor produces 800 kg×1.15=920 kg800 \text{ kg} \times 1.15 = 920 \text{ kg} of new fissile material per year. Looking at the incorrect options: B (680 kg) represents a common error where students might divide instead of multiply (800÷1.15≈696800 ÷ 1.15 ≈ 696), misunderstanding what the breeding ratio means. C (1150 kg) occurs if you mistakenly think the breeding ratio is additive rather than multiplicative - incorrectly calculating 800+(0.15×1000)=950800 + (0.15 \times 1000) = 950 or similar confused arithmetic. D (1380 kg) suggests adding the consumed amount to the produced amount (800+580800 + 580), but the question asks specifically for new material produced, not total material handled. The key insight is that breeding ratio is always multiplicative: new fissile material produced = consumed material × breeding ratio. When you see nuclear reactor problems involving breeding ratios, remember this direct relationship - don't overcomplicate with addition or division. The breeding ratio greater than 1.0 indicates the reactor produces more fuel than it consumes, which is the defining characteristic of breeder reactors.

Question 13

Consider a chain reaction where the reproduction factor k is exactly 1. If 1000 fission events occur in one generation of the chain reaction, how many fission events will occur ten generations later?

  1. 1000 (correct answer)
  2. 10000
  3. 1000 × 10¹⁰
  4. The number is unpredictable due to the random nature of fission.
Explanation: A reproduction factor k = 1 signifies a critical state. This means that, on average, each generation of fissions produces exactly the right number of neutrons to initiate the same number of fissions in the next generation. Therefore, the rate of reaction is constant. If there are 1000 fissions in one generation, there will be 1000 fissions in the next generation, and 1000 fissions ten generations later. The power output is stable.

Question 14

In a thermal nuclear reactor operating at a stable power output, the moderator is suddenly removed. What is the most likely immediate consequence for the chain reaction?

  1. The rate of fission increases rapidly because neutrons travel faster and collide with more nuclei.
  2. The rate of fission decreases significantly because fast neutrons are unlikely to induce fission in Uranium-235. (correct answer)
  3. The rate of fission remains unchanged, but the energy released per fission event increases.
  4. The rate of fission remains unchanged, but the reactor's temperature rises due to a lack of cooling.
Explanation: The moderator's function is to slow down fast neutrons produced during fission to thermal energies. Uranium-235 has a much higher fission cross-section (probability of fission) for thermal neutrons than for fast neutrons. Without the moderator, the neutrons remain fast, the probability of them inducing further fission drops dramatically, and the chain reaction effectively stops. Therefore, the rate of fission decreases significantly.

Question 15

A nuclear reactor is operating with a neutron reproduction factor k = 1.005. Which statement best describes the state of the reactor?

  1. The reactor is subcritical, and the power output is decreasing exponentially.
  2. The reactor is critical, and the power output is constant.
  3. The reactor is supercritical, and the power output is increasing. (correct answer)
  4. The reactor is in a runaway state, and an explosion is imminent.
Explanation: The neutron reproduction factor, k, is the average number of neutrons from one fission that cause a subsequent fission. If k > 1, the reactor is supercritical, and the number of fissions (and thus power output) increases with each generation. If k < 1, it is subcritical (power decreases). If k = 1, it is critical (power is stable). A value of k = 1.005 represents a controlled increase in power, not an imminent explosion.

Question 16

A substance is being evaluated for use as a moderator in a thermal nuclear reactor. Which combination of nuclear properties is most desirable?

  1. High probability of neutron absorption and large atomic mass.
  2. Low probability of neutron absorption and large atomic mass.
  3. High probability of neutron absorption and small atomic mass.
  4. Low probability of neutron absorption and small atomic mass. (correct answer)
Explanation: A moderator must slow down neutrons without absorbing them. To slow them down effectively, neutrons should collide with nuclei of similar mass; therefore, a small atomic mass is desirable (e.g., hydrogen in water, carbon in graphite). To ensure neutrons are available for the chain reaction, the moderator must not absorb them, requiring a low neutron absorption cross-section (low probability of absorption).

Question 17

For a self-sustaining chain reaction to be maintained in a mass of fissile material, a critical mass is required. Why does a sub-critical mass fail to sustain a chain reaction?

  1. The density is too low for neutrons to collide with nuclei.
  2. The temperature is too low to provide the activation energy for fission.
  3. The rate of neutron loss from the surface is greater than the rate of neutron production in the volume. (correct answer)
  4. The binding energy per nucleon is too high to allow for fission to occur.
Explanation: Neutron production is proportional to the volume of the fissile material (which scales with radius cubed, r³), while neutron loss (escape from the mass) is proportional to the surface area (which scales with r²). In a small, sub-critical mass, the surface-area-to-volume ratio is high, and more neutrons escape than are produced, so the chain reaction dies out (k < 1). At critical mass, production and loss rates balance (k = 1).

Question 18

In the context of a nuclear power plant, what is the function of the heat exchanger?

  1. It converts the kinetic energy of fission fragments directly into electrical energy via thermionic emission.
  2. It transfers thermal energy from the primary coolant loop to a secondary loop, typically to produce steam. (correct answer)
  3. It cools the control rods by circulating a fluid through them to prevent them from melting under high neutron flux.
  4. It moderates neutrons by exchanging their kinetic energy with the thermal energy of the surrounding fluid.
Explanation: The heat exchanger (often called a steam generator) serves as the interface between the radioactive primary coolant loop, which circulates through the reactor core, and the non-radioactive secondary loop. The hot primary coolant transfers its thermal energy to the water in the secondary loop, causing it to boil and produce high-pressure steam. This steam then drives the turbines to generate electricity.

Question 19

Cadmium and Boron are common materials used for control rods in nuclear reactors. What specific nuclear property makes them suitable for this purpose?

  1. They are excellent moderators, efficiently slowing neutrons to thermal speeds.
  2. They have a very high cross-section for absorbing thermal neutrons without undergoing fission. (correct answer)
  3. They are fissile materials that produce a predictable and small number of secondary neutrons.
  4. They have a high melting point and are very resistant to damage from prolonged radiation exposure.
Explanation: The function of a control rod is to regulate the neutron population in the reactor core. To do this effectively, the material must remove neutrons from the chain reaction. Cadmium and Boron have a very high probability (a large 'cross-section') of absorbing thermal neutrons. This absorption prevents the neutrons from causing further fission events. While engineering properties like heat resistance (D) are important, the key nuclear property is the high absorption cross-section.

Question 20

Which statement best explains why a single, isolated neutron is more likely to induce fission in U-235 than a single, isolated proton of the same kinetic energy?

  1. The proton is much heavier than the neutron and carries insufficient momentum.
  2. The proton does not interact via the strong nuclear force required to initiate fission.
  3. The proton is a stable particle, whereas the free neutron is unstable and decays before it can reach the nucleus.
  4. The proton is repelled by the electrostatic force of the nucleus, preventing it from getting close enough to be captured. (correct answer)
Explanation: To induce fission, the incident particle must be absorbed by the nucleus. The U-235 nucleus is strongly positive (92 protons). An incoming proton, also being positive, will experience a powerful electrostatic repulsion (Coulomb barrier) that it must overcome to reach the nucleus. A neutron, having no charge, does not experience this repulsion and can approach and be captured by the nucleus much more easily, even at very low (thermal) kinetic energies.