| Date | May 2012 | Marks available | 3 | Reference code | 12M.2.SL.TZ2.3 |
| Level | Standard level | Paper | Paper 2 | Time zone | Time zone 2 |
| Command term | Show that | Question number | 3 | Adapted from | N/A |
Question
This question is about nuclear reactions.
The nuclide U-235 is an isotope of uranium. A nucleus of U-235 undergoes radioactive decay to a nucleus of thorium-231 (Th-231). The proton number of uranium is 92.
(i) State what is meant by the terms nuclide and isotope.
-
Nuclide:
Isotope:
-
(ii) One of the particles produced in the decay of a nucleus of U-235 is a gamma photon. State the name of another particle that is also produced.
The daughter nuclei of U-235 undergo radioactive decay until eventually a stable isotope of lead is reached.
Explain why the nuclei of U-235 are unstable whereas the nuclei of the lead are stable.
Nuclei of U-235 bombarded with low energy neutrons can undergo nuclear fission. The nuclear reaction equation for a particular fission is shown below.
\[{}_0^1{\rm{n}} + {}_{92}^{235}{\rm{U}} \to {}_{56}^{144}{\rm{Ba}} + {}_{36}^{89}{\rm{Kr}} + 3{}_0^1{\rm{n}}\]
Show, using the following data, that the kinetic energy of the fission products is about 200 MeV.
Mass of nucleus of U-235 = 235.04393 u
Mass of nucleus of Ba-144 = 143.922952 u
Mass of nucleus of Kr-89 = 88.91763 u
Mass of neutron = 1.00867 u
Markscheme
(i) nuclide:
(a species of atom that is characterized by) the constitution of its nucleus /the number of protons and neutrons in the nucleus OWTTE;
isotope:
nuclides with the same proton number but different nucleon/neutron numbers;
or
atoms of the same element that have different numbers of neutrons/neutron number;
(ii) alpha particle / helium nucleus / \({}_2^4{\rm{He}}\);
protons repel/break nucleus apart;
binding energy/strong force holds nucleus together;
neutron excess / n:p ratio is greater in lead therefore overall balance of forces is
more attractive / (magnitude of) binding energy per nucleon is greater in lead /
binding energy per nucleon more negative in lead than uranium;
Δm=235.04393–[143.922952+88.91763+2×1.00867];
=0.1860u; (must see the u to award this mark)
energy=0.1860×931.5=173.9 MeV;
(≈ 200 MeV)
Examiners report
(i) A good statement of the meaning of nuclide was rare. Isotope was much better understood and explained.
(ii) The majority identified the alpha particle as the other particle in the reaction. Common errors included the neutron, various forms of neutrino, and the previously unknown alpha photon.
Candidates found it difficult to explain why U-235 is more unstable than a stable isotope of lead. It was rare to see clear statements of repulsive nature of the coulomb force and that it acts between protons whereas the strong nuclear force is attractive so that the balance of proton: neutron is changed in the more stable lead. Explanations in terms of binding energy per nucleon were also accepted. Explanations couched in terms of binding energy alone were usually incorrect.
SL only Calculations of the kinetic energy of the fission products in a nuclear reaction were carried through competently by many. Some however failed to show clearly the conversion from atomic mass units to electronvolts and lost some credit for this.
