HL Paper 2
A particular K meson has a quark structure s. State the charge, strangeness and baryon number for 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 and the direction of the arrows for the decay particles.
C-14 decay is used to estimate the age of an old dead tree. The activity of C-14 in the dead tree is determined to have fallen to 21% of its original value. C-14 has a half-life of 5700 years.
(i) Explain why the activity of C-14 in the dead tree decreases with time.
(ii) Calculate, in years, the age of the dead tree. Give your answer to an appropriate number of significant figures.
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
The energy in b(i) can be transferred into electrical energy to run the instruments of a spacecraft. A spacecraft carries 33 kg of pure plutonium-238 at launch. The decay constant of plutonium is 2.50 × 10−10 s−1.
Solar radiation falls onto a metallic surface carried by the spacecraft causing the emission of photoelectrons. The radiation has passed through a filter so it is monochromatic. The spacecraft is moving away from the Sun.
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.
Some unstable nuclei have many more neutrons than protons. Suggest the likely decay for these nuclei.
Show that the energy released in this decay is about 6 MeV.
The plutonium nucleus is at rest when it decays.
Calculate the ratio .
Estimate the power, in kW, that is available from the plutonium at launch.
The spacecraft will take 7.2 years (2.3 × 108 s) to reach a planet in the solar system. Estimate the power available to the spacecraft when it gets to the planet.
State and explain what happens to the kinetic energy of an emitted photoelectron.
State and explain what happens to the rate at which charge leaves the metallic surface.
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.
The specific energy of fossil fuel is typically . Suggest, with reference to your answer to (b)(i), one advantage of U-235 compared with fossil fuels in a power station.
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.
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.
The half-life of uranium-238 is about 4.5 × 109 years. The half-life of thallium-206 is about 4.2 minutes.
Compare and contrast the methods to measure these half-lives.
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.
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).
At the start of the experiment, Rutherford and Royds put 6.2 x 10–4 mol of pure radium-226 in a small closed cylinder A. Cylinder A is fixed in the centre of a larger closed cylinder B.
The experiment lasted for 6 days. The decay constant of radium-226 is 1.4 x 10–11 s–1.
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.
Write down the nuclear equation for this decay.
Deduce that the activity of the radium-226 is almost constant during the experiment.
Show that about 3 x 1015 alpha particles are emitted by the radium-226 in 6 days.
The wall of cylinder A is made from glass. Outline why this glass wall had to be very thin.
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 over the 6 day period. Helium is a monatomic gas.
Particles can be used in scattering experiments to estimate nuclear sizes.
Electron diffraction experiments indicate that the nuclear radius of carbon-12 is 2.7 x 10–15 m. The graph shows the variation of nuclear radius with nucleon number. The nuclear radius of the carbon-12 is shown on the graph.
The Feynman diagram shows electron capture.
State and explain the nature of the particle labelled X.
Outline how these experiments are carried out.
Outline why the particles must be accelerated to high energies in scattering experiments.
State and explain one example of a scientific analogy.
Plot the position of magnesium-24 on the graph.
Draw a line on the graph, to show the variation of nuclear radius with nucleon number.
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 unstable lead nuclide has a half-life of 15 × 106 years. A sample initially contains 2.0 μmol of the lead nuclide. Calculate the number of thallium nuclei being formed each second 30 × 106 years later.
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 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. The present activity of the sample is 8.0 × 10−3 Bq.
Determine, in years, the age of the sample.
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.
The temperature in the laboratory is higher than the temperature of the ice sample. Describe one other energy transfer that occurs between the ice sample and the laboratory.
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.
A low-pressure hydrogen discharge lamp contains a small amount of deuterium gas in addition to the hydrogen gas. The deuterium spectrum contains a red line with a wavelength very close to that of the hydrogen red line. The wavelengths for the principal lines in the visible spectra of deuterium and hydrogen are given in the table.
Light from the discharge lamp is normally incident on a diffraction grating.
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)(i).
Explain your answer to (a)(ii).
The light illuminates a width of 3.5 mm of the grating. The deuterium and hydrogen red lines can just be resolved in the second-order spectrum of the diffraction grating. Show that the grating spacing of the diffraction grating is about 2 × 10–6 m.
Calculate the angle between the first-order line of the red light in the hydrogen spectrum and the second-order line of the violet light in the hydrogen spectrum.
The light source is changed so that white light is incident on the diffraction grating. Outline the appearance of the diffraction pattern formed with white light.
is formed when a nucleus of deuterium () collides with a nucleus of . The radius of a deuterium nucleus is 1.5 fm.
State how the density of a nucleus varies with the number of nucleons in the nucleus.
Show that the nuclear radius of phosphorus-31 () is about 4 fm.
State the maximum distance between the centres of the nuclei for which the production of is likely to occur.
Determine, in J, the minimum initial kinetic energy that the deuterium nucleus must have in order to produce . Assume that the phosphorus nucleus is stationary throughout the interaction and that only electrostatic forces act.
undergoes beta-minus (β–) decay. Explain why the energy gained by the emitted beta particles in this decay is not the same for every beta particle.
State what is meant by decay constant.
In a fresh pure sample of the activity of the sample is 24 Bq. After one week the activity has become 17 Bq. Calculate, in s–1, the decay constant of .
Potassium-40 decays by two processes.
The first process is that of beta-minus (β−) decay to form a calcium (Ca) nuclide.
Potassium-40 decays by a second process to argon-40. This decay accounts for 11 % of the total decay of the potassium-40.
Rocks can be dated by measuring the quantity of argon-40 gas trapped in them. One rock sample contains 340 µmol of potassium-40 and 12 µmol of argon-40.
Write down the equation for this decay.
Show that the initial quantity of potassium-40 in the rock sample was about 450 µmol.
The half-life of potassium-40 is 1.3 × 109 years. Estimate the age of the rock sample.
Outline how the decay constant of potassium-40 was determined in the laboratory for a pure sample of the nuclide.
Rhodium-106 () decays into palladium-106 () by beta minus (β–) decay. The diagram shows some of the nuclear energy levels of rhodium-106 and palladium-106. The arrow represents the β– decay.
Bohr modified the Rutherford model by introducing the condition mvr = n. Outline the reason for this modification.
Show that the speed v of an electron in the hydrogen atom is related to the radius r of the orbit by the expression
where k is the Coulomb constant.
Using the answer in (b) and (c)(i), deduce that the radius r of the electron’s orbit in the ground state of hydrogen is given by the following expression.
Calculate the electron’s orbital radius in (c)(ii).
Explain what may be deduced about the energy of the electron in the β– decay.
Suggest why the β– decay is followed by the emission of a gamma ray photon.
Calculate the wavelength of the gamma ray photon in (d)(ii).