MYP Physics · topic MYP-17.05
Fission, chain reactions, and reactors
Connect the ideas, make your working visible, and test the result. Use the hints when you need a starting point; open the full solution after your attempt.
Extra challenging questions
Work through the linked stages and explain what each result means.
Balancing a fission channel and controlling a chain reaction
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]
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.
Show a hint
Begin with part (a): Find x and the multiplication factor in the example. Explain the distinct roles of moderator and control rods.
Reveal the worked solution
- 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.
Answer (a) x = 3; effective multiplication factor = 1.10; control must bring it toward 1 for steady operation. (b) Fission rate = 3.125×10¹⁹ s⁻¹.
Compare the assumptions, method and units with your attempt. Explain any correction before trying another question.