IB Physics HL E.4 Fission questions

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Question 1

Multiple choiceHard1 mark

A neutron initiates the reaction

{}^{1}_{0}\mathrm n+{}^{235}_{92}\mathrm U \rightarrow {}^{141}_{56}\mathrm{Ba}+{}^{92}_{36}\mathrm{Kr}+3\,{}^{1}_{0}\mathrm n .

Each fission releases three neutrons, and on average a fraction $r$ of neutrons from one generation cause a fission in the next, where $0<3r<1$ Let $m_{235}$ $m_{141}$ $m_{92}$ and $m_n$ be the nuclear masses of the indicated species. Which expression gives the expected total energy released by the complete chain?

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Answer: A. The mass defect per fission is $(m_{235}+m_n)-(m_{141}+m_{92}+3m_n)=m_{235}-m_{141}-m_{92}-2m_n$ so one fission releases $Q=\Delta mc^2$ Each fission produces an average of $3r$ further fissions. If $N$ is the expected total number of fissions, $N=1+3rN$ giving $N=1/(1-3r)$ The total expected energy is $NQ$

B: omits the net mass of the two additional neutrons in the products.
C: uses $r$ rather than $3r$ as the average number of further fissions per fission.
D: counts the initial fission and only its immediate descendants, omitting later generations.
Remember: the chain multiplication factor is the neutron yield per fission multiplied by the fraction that cause further fissions.

Question 2

Paper 2Hard10 marks

Figure 1 shows two fission channels with the same products. The masses shown are atomic masses; the electron numbers balance in each reaction. The incident neutron’s kinetic energy is $0.025\ \text{eV}$ Use $1\ \text{u}\,c^2=931.5\ \text{MeV}$

(a)

Calculate the energy released in the spontaneous fission reaction shown in Figure 1, in MeV.

[3]

(b)

Calculate the energy released in the neutron-induced fission reaction shown in Figure 1, in MeV.

[3]

(c)

A student claims that the greater energy release calculated for neutron-induced fission is supplied by the incident neutron’s kinetic energy. Assess this claim using Figure 1 and your answers. Include a quantitative comparison and account for the difference between the two energy releases.

[4]

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