SL Paper 2
Plutonium-238 (Pu) decays by alpha (α) decay into uranium (U).
The following data are available for binding energies per nucleon:
plutonium 7.568 MeV
uranium 7.600 MeV
alpha particle 7.074 MeV
State what is meant by the binding energy of a nucleus.
Draw, on the axes, a graph to show the variation with nucleon number of the binding energy per nucleon, . Numbers are not required on the vertical axis.
Identify, with a cross, on the graph in (a)(ii), the region of greatest stability.
Show that the energy released in this decay is about 6 MeV.
The plutonium nucleus is at rest when it decays.
Calculate the ratio .
A particular K meson has a quark structure s. State the charge on this meson.
The Feynman diagram shows the changes that occur during beta minus (β–) decay.
Label the diagram by inserting the four missing particle symbols.
Carbon-14 (C-14) is a radioactive isotope which undergoes beta minus (β–) decay to the stable isotope nitrogen-14 (N-14). Energy is released during this decay. Explain why the mass of a C-14 nucleus and the mass of a N-14 nucleus are slightly different even though they have the same nucleon number.
A possible decay of a lambda particle () is shown by the Feynman diagram.
State the quark structures of a meson and a baryon.
Explain which interaction is responsible for this decay.
Draw arrow heads on the lines representing and d in the .
Identify the exchange particle in this decay.
Outline one benefit of international cooperation in the construction or use of high-energy particle accelerators.
One possible fission reaction of uranium-235 (U-235) is
Mass of one atom of U-235
Binding energy per nucleon for U-235
Binding energy per nucleon for Xe-140
Binding energy per nucleon for Sr-94
A nuclear power station uses U-235 as fuel. Assume that every fission reaction of U-235 gives rise to of energy.
A sample of waste produced by the reactor contains of strontium-94 (Sr-94). Sr-94 is radioactive and undergoes beta-minus () decay into a daughter nuclide X. The reaction for this decay is
.
The graph shows the variation with time of the mass of Sr-94 remaining in the sample.
State what is meant by binding energy of a nucleus.
Outline why quantities such as atomic mass and nuclear binding energy are often expressed in non-SI units.
Show that the energy released in the reaction is about .
Estimate, in , the specific energy of U-235.
The power station has a useful power output of and an efficiency of . Determine the mass of U-235 that undergoes fission in one day.
Write down the proton number of nuclide X.
State the half-life of Sr-94.
Calculate the mass of Sr-94 remaining in the sample after minutes.
The first scientists to identify alpha particles by a direct method were Rutherford and Royds. They knew that radium-226 () decays by alpha emission to form a nuclide known as radon (Rn).
Write down the missing values in the nuclear equation for this decay.
Rutherford and Royds put some pure radium-226 in a small closed cylinder A. Cylinder A is fixed in the centre of a larger closed cylinder B.
At the start of the experiment all the air was removed from cylinder B. The alpha particles combined with electrons as they moved through the wall of cylinder A to form helium gas in cylinder B.
The wall of cylinder A is made from glass. Outline why this glass wall had to be very thin.
Rutherford and Royds expected 2.7 x 1015 alpha particles to be emitted during the experiment. The experiment was carried out at a temperature of 18 °C. The volume of cylinder B was 1.3 x 10–5 m3 and the volume of cylinder A was negligible. Calculate the pressure of the helium gas that was collected in cylinder B.
Rutherford and Royds identified the helium gas in cylinder B by observing its emission spectrum. Outline, with reference to atomic energy levels, how an emission spectrum is formed.
The work was first reported in a peer-reviewed scientific journal. Outline why Rutherford and Royds chose to publish their work in this way.
A stationary nucleus of uranium-238 undergoes alpha decay to form thorium-234.
The following data are available.
Energy released in decay 4.27 MeV
Binding energy per nucleon for helium 7.07 MeV
Binding energy per nucleon for thorium 7.60 MeV
Radioactive decay is said to be “random” and “spontaneous”. Outline what is meant by each of these terms.
Random:
Spontaneous:
Calculate the binding energy per nucleon for uranium-238.
Calculate the ratio .
Radioactive uranium-238 produces a series of decays ending with a stable nuclide of lead. The nuclides in the series decay by either alpha (α) or beta-minus (β−) processes.
The graph shows the variation with the nucleon number A of the binding energy per nucleon.
Uranium-238 decays into a nuclide of thorium-234 (Th).
Write down the complete equation for this radioactive decay.
Thallium-206 decays into lead-206 .
Identify the quark changes for this decay.
Outline why high temperatures are required for fusion to occur
Outline, with reference to the graph, why energy is released both in fusion and in fission.
Uranium-235 () is used as a nuclear fuel. The fission of uranium-235 can produce krypton-89 and barium-144.
Determine, in MeV and using the graph, the energy released by this fission.
Rhodium-106 () decays into palladium-106 () by beta minus (β–) decay.
The binding energy per nucleon of rhodium is 8.521 MeV and that of palladium is 8.550 MeV.
β– decay is described by the following incomplete Feynman diagram.
Rutherford constructed a model of the atom based on the results of the alpha particle scattering experiment. Describe this model.
State what is meant by the binding energy of a nucleus.
Show that the energy released in the β– decay of rhodium is about 3 MeV.
Draw a labelled arrow to complete the Feynman diagram.
Identify particle V.
The radioactive nuclide beryllium-10 (Be-10) undergoes beta minus (β–) decay to form a stable boron (B) nuclide.
The initial number of nuclei in a pure sample of beryllium-10 is N0. The graph shows how the number of remaining beryllium nuclei in the sample varies with time.
An ice sample is moved to a laboratory for analysis. The temperature of the sample is –20 °C.
Identify the missing information for this decay.
On the graph, sketch how the number of boron nuclei in the sample varies with time.
After 4.3 × 106 years,
Show that the half-life of beryllium-10 is 1.4 × 106 years.
Beryllium-10 is used to investigate ice samples from Antarctica. A sample of ice initially contains 7.6 × 1011 atoms of beryllium-10. State the number of remaining beryllium-10 nuclei in the sample after 2.8 × 106 years.
State what is meant by thermal radiation.
Discuss how the frequency of the radiation emitted by a black body can be used to estimate the temperature of the body.
Calculate the peak wavelength in the intensity of the radiation emitted by the ice sample.
Derive the units of intensity in terms of fundamental SI units.
During electron capture, an atomic electron is captured by a proton in the nucleus. The stable nuclide thallium-205 () can be formed when an unstable lead (Pb) nuclide captures an electron.
Write down the equation to represent this decay.
The neutron number N and the proton number Z are not equal for the nuclide . Explain, with reference to the forces acting within the nucleus, the reason for this.
Thallium-205 () can also form from successive alpha (α) and beta-minus (β−) decays of an unstable nuclide. The decays follow the sequence α β− β− α. The diagram shows the position of on a chart of neutron number against proton number.
Draw four arrows to show the sequence of changes to N and Z that occur as the forms from the unstable nuclide.
The diagram shows the position of the principal lines in the visible spectrum of atomic hydrogen and some of the corresponding energy levels of the hydrogen atom.
Determine the energy of a photon of blue light (435nm) emitted in the hydrogen spectrum.
Identify, with an arrow labelled B on the diagram, the transition in the hydrogen spectrum that gives rise to the photon with the energy in (a).
Explain your answer to (b).
Silicon-30 can be formed from phosphorus-30 by a process of beta-plus decay.
Write down the nuclear equation that represents this reaction.
Sketch the Feynman diagram that represents this reaction. The diagram has been started for you.
Energy is transferred to a hadron in an attempt to separate its quarks. Describe the implications of quark confinement for this situation.
The Standard Model was accepted by many scientists before the observation of the Higgs boson was made.
Outline why it is important to continue research into a topic once a scientific model has been accepted by the scientific community.
Describe the quark structure of a baryon.
The Feynman diagram shows a possible decay of the K+ meson.
Identify the interactions that are involved at points A and B in this decay.
The K+ meson can decay as
K+ → μ+ + vμ.
State and explain the interaction that is responsible for this decay.
Deuterium, , undergoes fusion according to the following reaction.
The following data are available for binding energies per nucleon.
Particle Y is produced in the collision of a proton with a K- in the following reaction.
The quark content of some of the particles involved are
Identify particle X.
Determine, in MeV, the energy released.
Suggest why, for the fusion reaction above to take place, the temperature of deuterium must be very high.
Identify, for particle Y, the charge.
Identify, for particle Y, the strangeness.
An experiment is carried out to determine the count rate, corrected for background radiation, when different thicknesses of copper are placed between a radioactive source and a detector. The graph shows the variation of corrected count rate with copper thickness.
Outline how the count rate was corrected for background radiation.
When a single piece of thin copper foil is placed between the source and detector, the count rate is 810 count minute−1. The foil is replaced with one that has three times the thickness. Estimate the new count rate.
Further results were obtained in this experiment with copper and lead absorbers.
Comment on the radiation detected from this radioactive source.
Another radioactive source consists of a nuclide of caesium that decays to barium .
Write down the reaction for this decay.
Conservation of energy and conservation of momentum are two examples of conservation laws.
Outline the significance of conservation laws for physics.
When a pi meson π- (du̅) and a proton (uud) collide, a possible outcome is a sigma baryon Σ0 (uds) and a kaon meson Κ0 (ds̅).
Apply three conservation laws to show that this interaction is possible.
The Feynman diagram shows electron capture.
Deduce that X must be an electron neutrino.
Distinguish between hadrons and leptons.