MYP · 17 · extended response
Balancing a fission channel and controlling a chain reaction
Atomic and nuclear physics · Original GioPhysics question with a detailed, mark-by-mark answer guide.
- Demand
- discriminating
- Marks
- 6
- Topics
- 2
- Answer
- Complete
Illustrative neutron multiplication
Supplied question data. Read the labelled axes and use the observations to test the physical model.
Vertical axis (y): Neutrons in relative units
Horizontal axis (x): Generation
Read the exact data as a table
| Generation | Neutrons in relative units |
|---|---|
| 0 | 100 |
| 1 | 110 |
| 2 | 121 |
| 3 | 133.1 |
These are the supplied values, not a worked answer. No fitted trend is drawn.
Optional enrichment: this challenge may extend beyond the usual syllabus depth and assumes confidence with algebra and graph interpretation. Consider the idealised fission channel ²³⁵₉₂U + ¹₀n → ¹⁴¹₅₆Ba + ⁹²₃₆Kr + x¹₀n. Each fission releases 200 MeV; 1 eV = 1.60×10⁻¹⁹ J. An illustrative reactor's successive-generation neutron population is supplied, with each generation lasting the same time. Supplied data (Generation; Neutrons in relative units): (0, 100), (1, 110), (2, 121), (3, 133.1).
- (a)
Find x and the multiplication factor in the example. Explain the distinct roles of moderator and control rods.
3 marks - (b)
Calculate the fission rate for 1.0 GW thermal output and explain the origin of the released energy.
3 marks
Ready to self-mark?Reveal the detailed answer guide
(a)
Find x and the multiplication factor in the example. Explain the distinct roles of moderator and control rods.
Build a chain of claim, evidence and physics reasoning. Address more than one relevant factor, identify a limitation or assumption, and finish with a conclusion that is conditional on the evidence rather than absolute.
- 1
Nucleon number gives 235+1 = 141+92+x, hence x = 3. Charge checks as 92 = 56+36; neutrons carry no charge.
- 2
The measured population ratio is 110/100 = 121/110 = 1.10, so this illustrative sequence grows by 10% per generation.
- 3
A moderator slows neutrons in a thermal reactor without being intended to absorb many; control rods absorb neutrons to adjust the effective multiplication. These functions are not interchangeable.
(b)
Calculate the fission rate for 1.0 GW thermal output and explain the origin of the released energy.
Build a chain of claim, evidence and physics reasoning. Address more than one relevant factor, identify a limitation or assumption, and finish with a conclusion that is conditional on the evidence rather than absolute.
- 1
Energy per fission is 200×10⁶×1.60×10⁻¹⁹ = 3.20×10⁻¹¹ J.
- 2
Rate = power/energy per event = 1.0×10⁹/(3.20×10⁻¹¹) = 3.125×10¹⁹ fissions s⁻¹.
- 3
The products have lower total rest mass and greater total binding energy; the mass difference appears as released energy. Nucleon and charge conservation do not imply equality of the sum of the separate rest masses.
Complete marking guidance
Use these worked steps alongside the part-by-part answers. They explain the method and mark allocation; they do not add extra marks.
- Nucleon number gives 235+1 = 141+92+x, hence x = 3. Charge checks as 92 = 56+36; neutrons carry no charge.
- The measured population ratio is 110/100 = 121/110 = 1.10, so this illustrative sequence grows by 10% per generation.
- A moderator slows neutrons in a thermal reactor without being intended to absorb many; control rods absorb neutrons to adjust the effective multiplication. These functions are not interchangeable.
- Energy per fission is 200×10⁶×1.60×10⁻¹⁹ = 3.20×10⁻¹¹ J.
- Rate = power/energy per event = 1.0×10⁹/(3.20×10⁻¹¹) = 3.125×10¹⁹ fissions s⁻¹.
- The products have lower total rest mass and greater total binding energy; the mass difference appears as released energy. Nucleon and charge conservation do not imply equality of the sum of the separate rest masses.
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