Nuclear Fission & Fusion (OCR A Level Physics): Exam Questions

A researcher is doing an experiment on a radioactive solution in a thin glass tube. The solution has two radioactive materials X and Y. The table below shows some data on these two materials.

The solution has the same number of nuclei of X and Y at the start.

i) State and explain which material has the greatest activity at the start.

[1]

ii) State why it is dangerous for the researcher to handle the test tube with bare hands.

[1]

Carbon-14 $\left({}_6{}^{14}\mathrm{C}\right)$ is produced in the upper atmosphere of the Earth by collisions between nitrogen nuclei and fast-moving neutrons. The nuclear transformation equation below shows the formation of a single carbon-14 nucleus.

${}_7{}^{14}\mathrm{N}+{}_0{}^1\mathrm{n}\to {}_6{}^{14}\mathrm{C}+\mathrm{X}$

i) State the proton number of particle X.

proton number = .......................................................... [1]

ii) Use the data below to determine the binding energy per nucleon of the 146C nucleus.

Write your answer to 3 significant figures.

• mass of neutron = 1.675 × 10^–27 kg

• mass of proton = 1.673 × 10^–27 kg

• mass of ${}_6{}^{14}\mathrm{C}$ nucleus = 14.000 u

• 1 u = 1.66 × 10^–27 kg

binding energy per nucleon = ................................... J per nucleon [4]

Fig. 21 shows stable and unstable nuclei of some light elements plotted on a grid. This grid has number of neutrons N on the vertical axis and number of protons Z on the horizontal axis.

Fig. 21

The key on Fig. 21 shows whether a nucleus is stable, emits a beta-plus particle or emits a beta-minus particle to become stable. For Z = 7, suggest in terms of N why an isotope may emit

i) a beta-minus particle [1]

ii) a beta-plus particle. [1]

Inside a nuclear reactor, fission reactions are controlled and chain reactions are prevented. A typical fission reaction of the uranium-235 nucleus (${}_{92}{}^{235}\mathrm{U}$) is illustrated below.

${}_0{}^1\mathrm{n}+{}_{92}{}^{235}\mathrm{U}\to {}_{55}{}^{141}\mathrm{Cs}+{}_{37}{}^{93}\mathrm{Rb}+2_0^1\mathrm{n}$

The neutron triggering the fission reaction moves slowly. The neutrons produced in the fission reaction move fast.

i) Describe what is meant by chain reaction.

[2]

ii) Explain how chain reactions are prevented inside a nuclear reactor.

[2]

iii) The energy released in each fission reaction is equivalent to a decrease in mass of 0.19u.

A fuel rod in a nuclear reactor contains 3.0% of uranium-235 by mass. Estimate the total energy produced from 1.0 kg of fuel rod. molar mass of uranium-235 = 0.235 kg mol^–1 1u = 1.66 × 10^–27 kg

energy = .......................................... J  [4]

Stars produce energy by nuclear fusion. One particular fusion reaction between two protons (${}_1{}^1\mathrm{H}$) is shown below.

${}_1{}^1\mathrm{H}+{}_1{}^1\mathrm{H}\to {}_1{}^2\mathrm{H}+{}_{+1}{}^0\mathrm{e}+\mathrm{v}$

In this reaction 2.2 MeV of energy is released.

Only one of the particles shown in the reaction has binding energy. Determine the binding energy per nucleon of this particle. Explain your answer.

[2]

Explain why high temperatures are necessary for fusion reactions to occur in stars.

[2]

A gamma photon in a star can spontaneously create an electron-positron pair. Calculate the maximum wavelength of a gamma photon for this creation event.

maximum wavelength = ......................................... m [3]

Describe the process of induced fission.

The following nuclear fission reaction occurs in a nuclear reactor.

${}_0{}^1\mathrm{n}+{}_{92}{}^{235}\mathrm{U}\to {}_{36}{}^{92}\mathrm{Kr}+{}_{56}{}^{141}\mathrm{Ba}+x{}_0{}^1\mathrm{n}$

The binding energy per nucleon of each isotope is given in the table below. 

(i) Determine the number $x$ of neutrons released in this reaction.

[1]

(ii) Suggest why the neutron is not included in the table.

[1]

(iii) Use the data to calculate the energy, in MeV, released in this reaction.

[2]

The radioactive isotope uranium−238 decays in a decay series to the stable lead−206. 

The half−life of ${}_{92}{}^{238}\mathrm{U}$ is 4.5 × 10⁹ years, which is much larger than all the other half−lives of the decays in the series.

A rock sample, when formed originally, contained 6.0 × 10²² atoms of ${}_{92}{}^{238}\mathrm{U}$ and no ${}_{82}{}^{206}\mathrm{Pb}$ atoms. At any given time, most of the atoms are either ${}_{92}{}^{238}\mathrm{U}$ or ${}_{82}{}^{206}\mathrm{Pb}$ with a negligible number of atoms in other forms in the decay series.

Sketch on the axes below the variation of number of ${}_{92}{}^{238}\mathrm{U}$ atoms and the number of ${}_{82}{}^{206}\mathrm{Pb}$ atoms in the rock sample as they vary over a period of 1.0 × 10¹⁰ years from its formation. Label the lines U and Pb.

A certain time, t, after its formation, the sample contained twice as many ${}_{92}{}^{238}\mathrm{U}$ atoms as ${}_{82}{}^{206}\mathrm{Pb}$ atoms. 

Show that the number of ${}_{92}{}^{238}\mathrm{U}$ atoms in the rock sample at time t was 4.0 × 10²².

Lead−214 is an unstable isotope of lead−206. It decays by emitting a ${\beta }^{-}$ particle to form bismuth−214 (Bi) 

Bismuth is also unstable and has two decay modes: 

• Emitting an α particle to form thallium−210 (Tl) + energy

• Emitting a β particle to form polonium−214 (Po) + energy

(i) Write decay equations for the decay chain of lead−214 to thallium−210 and to polonium−214.

[3]

(ii) Describe how energy released during this process.

[2]

When a uranium–235 nucleus undergoes fission, one of the possible reactions is: 

${}_{92}{}^{235}\mathrm{U}+{}_0{}^1\mathrm{n}\to {}_{54}{}^{139}\mathrm{Xe}+{}_{38}{}^{95}\mathrm{Sr}+2{}_0{}^1\mathrm{n}(+\mathrm{energy})$

A 1500 MW nuclear reactor, operating at 27% efficiency, uses enriched fuel containing 3% uranium–235 and 97% uranium–238.

The molar mass of uranium−235 is 0.235 kg mol^–1.

The energy released per fission of a uranium-235 nucleus in this reaction is 210 MeV.

(i) Estimate the total mass of original fuel required per year in the nuclear reactor. 

[4]

(ii) Explain why the value you have calculated for the mass of fuel required per year should be considered an estimate rather than an exact value, and state how the estimate may differ from the actual value.

[3]