
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 .
Markscheme
the energy needed to «completely» separate the nucleons of a nucleus
OR
the energy released when a nucleus is assembled from its constituent nucleons ✓
Accept reference to protons AND neutrons.
curve rising to a maximum between 50 and 100 ✓
curve continued and decreasing ✓
Ignore starting point.
Ignore maximum at alpha particle
At a point on the peak of their graph ✓
correct mass numbers for uranium (234) and alpha (4) ✓
«MeV» ✓
energy released 5.51 «MeV» ✓
Ignore any negative sign.
«» OR ✓
«» ✓
Award [2] marks for a bald correct answer.
Accept for MP2.
Examiners report
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.
Markscheme
charge: –1«e» or negative or K−
Negative signs required.
correct symbols for both missing quarks
exchange particle and electron labelled W or W– and e or e–
Do not allow W+ or e+ or β+ Allow β or β–
decay products include an electron that has mass
OR
products have energy that has a mass equivalent
OR
mass/mass defect/binding energy converted to mass/energy of decay products
«so»
mass C-14 > mass N-14
OR
mass of n > mass of p
OR
mass of d > mass of u
Accept reference to “lighter” and “heavier” in mass.
Do not accept implied comparison, eg “C-14 has greater mass”. Comparison must be explicit as stated in scheme.
Examiners report
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.
Markscheme
Meson: quark-antiquark pair
Baryon: 3 quarks
Alternative 1
strange quark changes «flavour» to an up quark
changes in quarks/strangeness happen only by the weak interaction
Alternative 2
Strangeness is not conserved in this decay «because the strange quark changes to an up quark»
Strangeness is not conserved during the weak interaction
Do not allow a bald answer of weak interaction.
arrows drawn in the direction shown
Both needed for [1] mark.
W −
Do not allow W or W+.
it lowers the cost to individual nations, as the costs are shared
international co-operation leads to international understanding OR historical example of co-operation OR co-operation always allows science to proceed
large quantities of data are produced that are more than one institution/research group can handle co-operation allows effective analysis
Any one.
Examiners report
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.
Markscheme
energy required to «completely» separate the nucleons
OR
energy released when a nucleus is formed from its constituent nucleons ✓
Allow protons AND neutrons.
the values «in SI units» would be very small ✓
OR ✓
see AND ✓
✓
energy produced in one day ✓
mass ✓
✓
Do not allow unless the proton number is indicated.
✓
ALTERNATIVE 1
✓
mass remaining ✓
ALTERNATIVE 2
decay constant ✓
mass remaining ✓
Examiners report
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.
Markscheme
222 AND 4
Both needed.
alpha particles highly ionizing
OR
alpha particles have a low penetration power
OR
thin glass increases probability of alpha crossing glass
OR
decreases probability of alpha striking atom/nucleus/molecule
conversion of temperature to 291 K
p = 4.5 x 10–9 x 8.31 x «»
OR
p = 2.7 x 1015 x 1.38 x 10–23 x «»
0.83 or 0.84 «Pa»
electron/atom drops from high energy state/level to low state
energy levels are discrete
wavelength/frequency of photon is related to energy change or quotes E = hf or E =
and is therefore also discrete
peer review guarantees the validity of the work
OR
means that readers have confidence in the validity of work
OWTTE
Examiners report
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 .
Markscheme
random:
it cannot be predicted which nucleus will decay
OR
it cannot be predicted when a nucleus will decay ✔
NOTE: OWTTE
spontaneous:
the decay cannot be influenced/modified in any way ✔
NOTE: OWTTE
234 × 7.6 OR 4 × 7.07 ✔
BEU =« 234 × 7.6 + 4 × 7.07 – 4.27 =» « MeV » ✔
« MeV » ✔
NOTE: Allow ECF from MP2
Award [3] for bald correct answer
Allow conversion to J, final answer is 1.2 × 10–12
states or applies conservation of momentum ✔
ratio is «» 58.5 ✔
NOTE: Award [2] for bald correct answer
Examiners report
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.
Markscheme
✓
Allow He for alpha.
udd→uud
OR
down quark changes to up quark ✓
links temperature to kinetic energy/speed of particles ✓
energy required to overcome «Coulomb» electrostatic repulsion ✓
«energy is released when» binding energy per nucleon increases
any use of (value from graph) x (number of nucleons) ✓
✓
Examiners report
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.
Markscheme
«most of» the mass of the atom is confined within a very small volume/nucleus
«all» the positive charge is confined within a very small volume/nucleus
electrons orbit the nucleus «in circular orbits»
[2 marks]
the energy needed to separate the nucleons of a nucleus
OR
energy released when a nucleus is formed from its nucleons
Allow neutrons AND protons for nucleons
Don’t allow constituent parts
[1 mark]
Q = 106 × 8.550 − 106 × 8.521 = 3.07 «MeV»
«Q ≈ 3 Me V»
[1 mark]
line with arrow as shown labelled anti-neutrino/
Correct direction of the “arrow” is essential
The line drawn must be “upwards” from the vertex in the time direction i.e. above the horizontal
[1 mark]
V = W–
[1 mark]
Examiners report
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.
Markscheme
conservation of mass number AND charge ,
Correct identification of both missing values required for [1].
[1 mark]
correct shape ie increasing from 0 to about 0.80 N0
crosses given line at 0.50 N0
[2 marks]
ALTERNATIVE 1
fraction of Be = , 12.5%, or 0.125
therefore 3 half lives have elapsed
«≈ 1.4 × 106» «y»
ALTERNATIVE 2
fraction of Be = , 12.5%, or 0.125
leading to λ = 4.836 × 10–7 «y»–1
= 1.43 × 106 «y»
Must see at least one extra sig fig in final answer.
[3 marks]
1.9 × 1011
[1 mark]
emission of (infrared) electromagnetic/infrared energy/waves/radiation.
[1 mark]
the (peak) wavelength of emitted em waves depends on temperature of emitter/reference to Wein’s Law
so frequency/color depends on temperature
[2 marks]
= 1.1 × 10–5 «m»
Allow ECF from MP1 (incorrect temperature).
[2 marks]
correct units for Intensity (allow W, Nms–1 OR Js–1 in numerator)
rearrangement into proper SI units = kgs–3
Allow ECF for MP2 if final answer is in fundamental units.
[2 marks]
Examiners report
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.
Markscheme
✓
✓
Reference to proton repulsion OR nucleon attraction ✓
strong force is short range OR electrostatic/electromagnetic force is long range ✓
more neutrons «than protons» needed «to hold nucleus together» ✓
any α change correct ✓
any β change correct ✓
diagram fully correct ✓
Award [2] max for a correct diagram without arrows drawn.
For MP1 accept a (−2, −2 ) line with direction indicated, drawn at any position in the graph.
For MP2 accept a (1, −1) line with direction indicated, drawn at any position in the graph.
Award [1] max for a correct diagram
Examiners report
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).
Markscheme
identifies λ = 435 nm ✔
E = « =» ✔
4.6 ×10−19 «J» ✔
–0.605 OR –0.870 OR –1.36 to –5.44 AND arrow pointing downwards ✔
Arrow MUST match calculation in (a)(i)
Allow ECF from (a)(i)
Difference in energy levels is equal to the energy of the photon ✔
Downward arrow as energy is lost by hydrogen/energy is given out in the photon/the electron falls from a higher energy level to a lower one ✔
Allow ECF from (a)(i)
Examiners report
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.
Markscheme
✔
✔
Subscript on neutrino not necessary to award MP2.
Allow the use of β for e.
Do not allow an anti-neutrino for MP2.
correct change of either u to d ✔
W+ shown ✔
correct arrow directions for positron and electron neutrino ✔
Allow ECF from MP2 in ai for MP3.
quarks cannot be directly observed as free particles/must remain bound to other quarks/quarks cannot be isolated ✔
because energy given to nucleon creates other particles rather than freeing quarks/OWTTE ✔
models need testing/new information may change models/new technology may bring new information/Models can be revised/OWTTE ✔
Look for responses that suggest changes/improvements to models.
Don’t accept answers specifically about the Standard Model.
Don’t accept answers about simply proving the model correct.
Examiners report
Few candidates were awarded full marks for a variety of reasons for the Feynman diagram they drew, and many left this question blank. It should be noted that on the exam the time axis can either be vertical or horizontal, so candidates should be familiar with both methods of drawing Feynman diagrams. Candidates should be able to draw Feynman diagrams from scratch either way. The examiners were looking for the basics of drawing a diagram (proper change in quark structure, proper exchange particle, and proper arrow directions for the positron and neutrino).
Few candidates recognized that quarks cannot exist in isolation, and fewer still could discuss the effect of adding energy to attempt to separate quarks. Some recognized that the added energy would ultimately be converted into mass, but few clearly specified that this would form new particles (such as mesons) rather than just new quarks.
This was a “nature of science” question. The examiners were looking for the idea that models can be improved on and revised by new data rather than just proven right or wrong.
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.
Markscheme
3 quarks / example with three quarks «e.g. up up down» ✓
integer / zero / 1 / no fractional «electron» charge
OR
held together by the strong force / gluons
OR
half integer spin
OR
baryon number = 1
OR
colour neutral ✓
A «Decay of the strange antiquark is a» weak «interaction» ✓
B «Decay of the u to a gluon and eventually to d and anti-d is a» strong «interaction» ✓
weak «interaction» ✓
strangeness is not conserved and this is possible only in weak interactions
OR
the weak interaction allows change of quark flavour
OR
only the weak interaction has a boson / an exchange particle / a W+ to conserve the charge
OR
neutrinos are only produced via the weak interaction ✓
Examiners report
A significant number of candidates recognized that baryons are composed of three quarks. The second mark was for a statement concerning baryons as a result of the quark composition, and not for a general statement about the quarks (e.g. "the baryon number is 1" rather than "each quark has a baryon number of ⅓). It is worth noting that the information about individual quarks is given in the data booklet which is why no marks were awarded for simply copying this information over.
Many candidates were able to successfully identify the two interactions in the diagram. Some candidates only described what was happening in the diagram without identifying the actual interaction. A common mistake was identifying the gluon at B as a graviton, and/or suggesting that this was a gravitational interaction. Many candidates also did not make the connection between the term "interaction" in the stem and the concept of force.
This was another item where some candidates simply described the particles without specifying the weak interaction. The second marking point was for a justification based on an aspect of this decay that could only be true of the weak nuclear force. A commonly incorrect answer was that this was the only force that acted on quarks and leptons, which was not accepted due to the fact that the gravitational force also acts on these particles as well. Another common incorrect answer among SL candidates was to assume that this was an example of beta negative decay due to the presence of a neutrino.
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.
Markscheme
proton / / p ✔
«3 x 2.78 − 2 × 2 × 1.12»
See 3 × 2.78/8.34 OR 2 × 2 × 1.12/4.48✔
3.86 «MeV» ✔
the deuterium nuclei are positively charged/repel ✔
high KE/energy is required to overcome «Coulomb/electrostatic» repulsion /potential barrier
OR
high KE/energy is required to bring the nuclei within range of the strong nuclear force ✔
high temperatures are required to give high KEs/energies ✔
−1 / -e ✔
−3 ✔
Examiners report
At HL this was well answered with the most common wrong answer being ‘neutron’. At SL however, this was surprisingly wrongly answered by many. Suggestions given included most smallish particles, alpha, positron, beta, antineutrino and even helium.
The majority of candidates missed the fact that the figures given were the binding energies per nucleon. Many complicated calculations were also seen, particularly at SL, that involved E = mc2.
The most common mark to be awarded here was the one for linking high temperature to high KE. A large number of candidates talked about having to overcome the strong nuclear force before fusion could happen.
At SL many answers of just ‘negative’ were seen.
This was poorly answered at both levels with the most common answer being zero.
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.
Markscheme
background count rate is subtracted «from each reading» ✓
OWTTE
thickness is 0.25 «mm» ✓
380 «count min−1» ✓
MP1 and MP2 can be shown on the graph
Allow a range of 0.23 to 0.27 mm for MP1
Allow ECF from MP1.
Accept a final answer in the range 350 – 420
lead better absorber than copper ✓
not alpha ✓
as it does not go through the foil / it is easily stopped / it is stopped by paper ✓
there is gamma ✓
as it goes through lead ✓
ALTERNATIVE 1
can be beta ✓
as it is attenuated by «thin» metal / can go through «thin» metal ✓
ALTERNATIVE 2
not beta ✓
it is stopped by «thin» metal ✓
✓
✓
Accept β or e in MP1.
Do not penalize if proton / nucleon numbers or electron subscript in antineutrino are missing.
Examiners report
a) A majority of candidates were able to say that background radiation count was subtracted from all readings.
b) A fairly easy question with most candidates being able to take readings from the graph to get a final count rate of approximately 380 counts per second. Many did not seem to have used a ruler to help their reading.
c) This was a bit chaotic with candidates showing all sorts of misconceptions. The first marking point was the one most commonly awarded. The 2 big misconceptions were that the copper and lead were radioactive themselves and produced the radiation, or that the higher the figures the better absorbers they were. Far too many candidates thought that the question was only about the radiation passing through the 3.5 mm of lead and copper. Most of these candidates realised that there must be some gamma radiation in the radiation detected. Far fewer stated that there could not be any alpha. Opinions varied as to whether there was beta, but any sensible answers were given credit.
d) This question was generally well answered, with most candidates getting
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.
Markscheme
they express fundamental principles of nature ✓
allow to model situations ✓
allow to calculate unknown variables ✓
allow to predict possible outcomes ✓
allow to predict missing quantities/particles ✓
allow comparison of different system states ✓
three correct conservation laws listed ✓
at least one conservation law correctly demonstrated ✓
all three conservation laws correctly demonstrated ✓
Examiners report
The Feynman diagram shows electron capture.
Deduce that X must be an electron neutrino.
Distinguish between hadrons and leptons.
Markscheme
it has a lepton number of 1 «as lepton number is conserved»
it has a charge of zero/is neutral «as charge is conserved»
OR
it has a baryon number of 0 «as baryon number is conserved»
Do not credit answers referring to energy
hadrons experience strong force
OR
leptons do not experience the strong force
hadrons made of quarks/not fundamental
OR
leptons are not made of quarks/are fundamental
hadrons decay «eventually» into protons
OR
leptons do not decay into protons
Accept leptons experience the weak force
Allow “interaction” for “force”