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school. “Paper 42” means Paper 4, variant 2.
Practice questions
Original questions written by HomiLabs in the style of the exam, with answers and mark schemes. They are not
Cambridge past paper questions and have not been reviewed by Cambridge. Try each one before opening the answer.
Q1Atoms, nuclei & radiation (alpha/beta/gamma, decay equations) · Core · Paper 1 style · 1 mark
(a)In the α-particle scattering experiment, a thin gold foil is bombarded with α-particles. Which observation shows that most of the volume of an atom is empty space?[1]
Show answer
(a) B Most of the α-particles pass through the foil with little or no deflection.
Almost all α-particles pass straight through, so most of the atom offers no obstruction: it is mostly empty space. A shows that the positive charge and most of the mass are concentrated in a tiny nucleus, not that the atom is mostly empty.
Q2Atoms, nuclei & radiation (alpha/beta/gamma, decay equations) · Core · Paper 1 style · 1 mark
(a)[1]
Show answer
(a) A ²³⁴₉₂U
α: A − 4, Z − 2 gives ²³⁴₉₀; each β⁻: Z + 1, A unchanged, so ²³⁴₉₂ (an isotope of uranium). ²³⁴₉₀Th is the nuclide after the α only.
Q3Atoms, nuclei & radiation (alpha/beta/gamma, decay equations) · Core · Paper 2 style · 5 marks
In the α-particle scattering experiment, α-particles from a source are directed at a very thin gold foil in a vacuum. A detector is moved around the foil to count the α-particles scattered through different angles.
(a)State two observations from the experiment and, for each, the conclusion drawn about the structure of the atom.[4]
(b)Explain why the foil used must be very thin.[1]
Show answer
(a) Most α-particles pass straight through → the atom is mostly empty space. A very small number are deflected through large angles (> 90°) → there is a tiny, dense nucleus that is positively charged and contains most of the mass.
B1 most undeflected; B1 mostly empty space / nucleus very small compared with the atom; B1 very few deflected through large angles; B1 nucleus is positive (repels α) and contains most of the mass (concentrated)
(b) So that each α-particle is scattered by at most one nucleus (and is not absorbed).
B1 α-particles have a short range / single scattering events only
Q4Atoms, nuclei & radiation (alpha/beta/gamma, decay equations) · Core · Paper 2 style · 5 marks
(a)For a neutral atom of the nuclide ⁵⁹₂₆Fe, state the number of (i) protons, (ii) neutrons, (iii) electrons.[2]
(b)Iron-56 is another isotope of iron. Explain what is meant by isotopes.[1]
(c)Iron-59 decays by β⁻ emission to form an isotope of cobalt (Co). Write a nuclear equation for the decay.[2]
(b) Nuclei of the same element with the same number of protons but different numbers of neutrons.
B1 same proton number, different nucleon (neutron) number
(c) ⁵⁹₂₆Fe → ⁵⁹₂₇Co + ⁰₋₁e + ν̄
B1 correct cobalt nuclide ⁵⁹₂₇Co; B1 β⁻ particle and antineutrino included with correct numbers
Q5Atoms, nuclei & radiation (alpha/beta/gamma, decay equations) · Core · Paper 2 style · 6 marks
A radioactive source emits α-particles, β⁻ particles and γ-radiation.
(a)State the charge of each type of radiation in terms of e.[2]
(b)State which type of radiation (i) is the most strongly ionising, (ii) travels at the speed of light, (iii) has a mass of about 4 u.[3]
(c)State the type of radiation that is not deflected by an electric field and explain why.[1]
Show answer
(a) α: +2e; β⁻: −e; γ: 0
B2 all three correct (B1 for two)
(b) (i) α (ii) γ (iii) α
B1 each
(c) γ-radiation, because it is uncharged (electromagnetic radiation).
B1
Q6Atoms, nuclei & radiation (alpha/beta/gamma, decay equations) · Core · Paper 2 style · 5 marks
(a)Write a nuclear equation for the β⁻ decay of cobalt-60 to nickel-60. Cobalt has proton number 27.[2]
(b)The nickel nucleus formed is in an excited state and then emits a γ-ray photon. State the effect of this emission on the proton number and nucleon number of the nucleus, and give a reason.[2]
(c)Cobalt-60 is used in hospitals to treat cancer. Suggest why the γ-radiation, not the β⁻ radiation, is used for treating a tumour deep inside the body.[1]
Show answer
(a) ⁶⁰₂₇Co → ⁶⁰₂₈Ni + ⁰₋₁e + ν̄
B1 ⁶⁰₂₈Ni; B1 electron and antineutrino
(b) Neither changes: a γ-photon has no charge and no mass; the nucleus only loses energy.
B1 no change to A or Z; B1 γ has no charge/mass, only energy is lost
(c) γ-radiation is much more penetrating and can reach the tumour; β⁻ is absorbed by a few mm of tissue.
B1
Q7Atoms, nuclei & radiation (alpha/beta/gamma, decay equations) · Standard · Paper 1 style · 1 mark
(a)The β⁻ particles emitted by a radioactive source have a continuous range of kinetic energies up to a maximum value. What is the reason for this?[1]
Show answer
(a) C The energy released in each decay is shared between the β⁻ particle and an antineutrino.
Each decay releases the same energy, but it is shared in varying proportions with an (electron) antineutrino, so the β⁻ energy varies continuously. A γ-photon (D) has a fixed energy and would not produce a continuous spectrum.
Q8Atoms, nuclei & radiation (alpha/beta/gamma, decay equations) · Standard · Paper 1 style · 1 mark
(a)[1]
Show answer
(a) A Z decreases by 1; A is unchanged
In β⁺ decay a proton changes into a neutron, emitting a positron and a neutrino: Z falls by 1, the number of nucleons stays the same. B describes β⁻ decay.
Q9Atoms, nuclei & radiation (alpha/beta/gamma, decay equations) · Standard · Paper 2 style · 7 marks
Radon-222 is a radioactive gas that can collect in poorly ventilated basements. It decays through a series of short-lived nuclides.
(a)Identify, with its proton number and nucleon number, each of the nuclides X, Y and Z in the chain below. Polonium is Po (84), lead is Pb (82) and bismuth is Bi (83).²²²₈₆Rn → (α) → X → (α) → Y → (β⁻) → Z[3]
(b)Z then decays by β⁻ emission. State the proton number and nucleon number of the product, and name the element.[2]
(c)Write the equation for the β⁻ decay of Y, including all the particles emitted.[2]
Show answer
(a) X = ²¹⁸₈₄Po; Y = ²¹⁴₈₂Pb; Z = ²¹⁴₈₃Bi
B1 each nuclide (A and Z both correct)
(b) Z = 84, A = 214: polonium-214
B1 84 and 214; B1 polonium
(c) ²¹⁴₈₂Pb → ²¹⁴₈₃Bi + ⁰₋₁e + ν̄
B1 nuclides; B1 electron and electron antineutrino
Q10Atoms, nuclei & radiation (alpha/beta/gamma, decay equations) · Standard · Paper 2 style · 5 marks
Smoke detectors contain americium-241, which emits α-particles. Each α-particle is emitted with a kinetic energy of about 5.5 MeV.
(a)Convert 5.5 MeV into joules. (1 eV = 1.60 × 10⁻¹⁹ J)[1]
(b)The mass of an α-particle is 4.0 u, where 1 u = 1.66 × 10⁻²⁷ kg. Calculate the initial speed of an α-particle.[3]
(c)State how the α-particle energies from americium-241 differ from the β⁻ energies from a β⁻ source.[1]
Show answer
(a) 8.8 × 10⁻¹³ J
5.5 × 10⁶ × 1.60 × 10⁻¹⁹ = 8.8 × 10⁻¹³ J (B1)
(b) 1.6 × 10⁷ m s⁻¹
m = 4.0 × 1.66 × 10⁻²⁷ = 6.64 × 10⁻²⁷ kg (C1); ½mv² = 8.8 × 10⁻¹³ (C1); v = 1.6 × 10⁷ m s⁻¹ (A1)
(c) α-particles from one decay have discrete (single) energies; β⁻ energies have a continuous range.
B1
Q11Atoms, nuclei & radiation (alpha/beta/gamma, decay equations) · Standard · Paper 2 style · 5 marks
A student places different absorbers between a radioactive source and a Geiger–Müller tube and measures the count rate. The background count rate is 30 counts per minute.absorber: none — count rate 520 min⁻¹absorber: sheet of paper — 516 min⁻¹absorber: 3 mm aluminium — 216 min⁻¹absorber: 2.5 cm lead — 94 min⁻¹
(a)Calculate the corrected count rate for each absorber.[2]
(b)Deduce, with reasons, which types of radiation the source emits.[3]
C1 subtract background 30 min⁻¹; A1 all four values correct
(b) No α: paper causes no significant drop. β present: 3 mm aluminium causes a large drop. γ present: the count through 2.5 cm of lead is still well above background.
B1 no α with reason; B1 β with reason; B1 γ with reason
Q12Atoms, nuclei & radiation (alpha/beta/gamma, decay equations) · Standard · Paper 2 style · 5 marks
Carbon-12 and carbon-14 are isotopes of carbon (proton number 6). Carbon-14 is used to date ancient wooden objects such as those found at Mohenjo-daro. Take 1 u = 1.66 × 10⁻²⁷ kg and e = 1.60 × 10⁻¹⁹ C, and treat the mass of each nucleus as A × u.
(a)Calculate the specific charge (charge/mass) of a carbon-12 nucleus.[2]
(b)Calculate the specific charge of a carbon-14 nucleus.[1]
(c)Explain, in terms of the particles in each nucleus, why the specific charges differ.[2]
(d) The nucleus is about 10¹³ times denser than the material: almost all the mass is in a tiny nucleus and the atom is mostly empty space.
B1 nuclear density ≫ density of gold (by ~10¹³); B1 mass concentrated in nucleus, atom mostly empty space
Q15Atoms, nuclei & radiation (alpha/beta/gamma, decay equations) · Challenge · Paper 2 style · 6 marks
Phosphorus-32 decays by β⁻ emission to sulfur-32. The total energy released in each decay is 1.71 MeV.
(a)An electron emitted by one phosphorus-32 nucleus has a kinetic energy of 0.65 MeV. Determine the energy carried away by the antineutrino. Assume the recoil energy of the nucleus is negligible.[2]
(b)Describe the shape of the energy spectrum of the β⁻ particles and explain why it has this shape.[3]
(c)Explain why α-particles emitted by one nuclide all have the same energy (discrete energy).[1]
Show answer
(a) 1.06 MeV
total energy released is the same for every decay = 1.71 MeV (C1); 1.71 − 0.65 = 1.06 MeV (A1)
(b) A continuous range of energies from (almost) zero up to 1.71 MeV, with most electrons having an intermediate energy; the energy released is shared in different proportions between the electron and the antineutrino.
B1 continuous range from 0 to maximum 1.71 MeV; B1 a fixed energy is released in each decay; B1 shared randomly with the antineutrino
(c) Only two particles are produced (α and daughter nucleus), so momentum and energy conservation fix the share: no third particle.
B1
Q16Atoms, nuclei & radiation (alpha/beta/gamma, decay equations) · Challenge · Paper 2 style · 5 marks
A narrow beam containing α-particles and β⁻ particles passes between two parallel metal plates in a vacuum. There is a uniform electric field between the plates.
(a)State the direction in which each type of particle is deflected.[1]
(b)Calculate the specific charge (charge/mass) of (i) a β⁻ particle (electron mass 9.11 × 10⁻³¹ kg), (ii) an α-particle (mass 4.0 u, 1 u = 1.66 × 10⁻²⁷ kg).[2]
(c)The β⁻ particles in this experiment are deflected much more than the α-particles. Use your answers to (b) to explain this, even though the β⁻ particle has a smaller charge.[2]
Show answer
(a) α towards the negative plate; β⁻ towards the positive plate.
Q20Fundamental particles (quarks, leptons, hadrons) · Core · Paper 2 style · 5 marks
(a)State two properties that are the same and one property that is different for an electron and a positron.[2]
(b)An antiparticle has the quark composition ū d̄ d̄. Determine its charge and name the particle of which it is the antiparticle.[2]
(c)Name the antiparticle produced in β⁻ decay.[1]
Show answer
(a) Same: mass (and magnitude of charge, spin); different: sign of charge (−e and +e).
B1 same mass and same magnitude of charge; B1 opposite charge
(b) charge 0; it is the antineutron (antiparticle of the neutron, udd)
B1 −⅔ + ⅓ + ⅓ = 0; B1 antineutron
(c) the electron antineutrino
B1
Q21Fundamental particles (quarks, leptons, hadrons) · Core · Paper 2 style · 4 marks
(a)Name two leptons.[1]
(b)State two differences between leptons and hadrons.[2]
(c)A proton and an electron have charges of equal magnitude. State why the proton is not a fundamental particle but the electron is.[1]
Show answer
(a) electron and electron neutrino (also positron, antineutrino)
B1
(b) Leptons are fundamental (not made of quarks); hadrons are made of quarks. Hadrons are affected by the strong force; leptons are not.
B1 leptons fundamental / hadrons made of quarks; B1 strong force acts on hadrons, not leptons
(c) The proton is made of three quarks (uud); the electron is not made of smaller particles.
B1
Q22Fundamental particles (quarks, leptons, hadrons) · Standard · Paper 1 style · 1 mark
(a)Which quark combination could be a baryon with a charge of −e?[1]
Show answer
(a) A d d s
A baryon has three quarks: d d s gives −⅓ −⅓ −⅓ = −1. ū d has charge −1 but is a quark–antiquark pair (a meson); u u s has charge +1; d s̄ is a neutral meson.
Q23Fundamental particles (quarks, leptons, hadrons) · Standard · Paper 2 style · 6 marks
(a)Write the equation for the β⁻ decay of a free neutron, including all the particles produced.[2]
(b)Describe the change in quark composition that takes place, and show that charge is conserved in this quark change.[3]
(c)Name the type of interaction responsible for β decay.[1]
Show answer
(a) ¹₀n → ¹₁p + ⁰₋₁e + ν̄
B1 proton and electron; B1 electron antineutrino
(b) d → u + e⁻ + ν̄: charge −⅓ = +⅔ + (−1) + 0
B1 udd → uud; B1 a down quark changes to an up quark; B1 charge check −⅓ = ⅔ − 1
(c) the weak interaction
B1
Q24Fundamental particles (quarks, leptons, hadrons) · Standard · Paper 2 style · 5 marks
Some baryons contain strange quarks.
(a)The Σ⁺ baryon has the quark composition u u s. Determine its charge in terms of e.[1]
(b)State the quark composition and the charge of the antiparticle of the Σ⁺.[2]
(c)The Ξ⁰ baryon has zero charge and contains two strange quarks. Deduce its quark composition.[2]
Show answer
(a) +e
B1 ⅔ + ⅔ − ⅓ = +1
(b) ū ū s̄; charge −e
B1 ū ū s̄; B1 −⅔ − ⅔ + ⅓ = −1
(c) u s s
M1 two s quarks give −⅔, so the third quark must have charge +⅔; A1 u s s
Q25Fundamental particles (quarks, leptons, hadrons) · Standard · Paper 2 style · 5 marks
(a)Carbon-11, ¹¹₆C, used in PET scanners, decays by β⁺ emission to an isotope of boron (B). Write the nuclear equation, including all particles.[2]
(b)State the change in quark flavour that occurs.[1]
(c)Identify which of the particles produced in (a) are leptons and which is an antiparticle.[2]
Show answer
(a) ¹¹₆C → ¹¹₅B + ⁰₊₁e + ν
B1 ¹¹₅B; B1 positron and electron neutrino
(b) an up quark changes to a down quark (u → d)
B1
(c) Leptons: positron and neutrino; the positron is an antiparticle (of the electron).
B1 positron and neutrino are leptons; B1 positron is the antiparticle
Q26Fundamental particles (quarks, leptons, hadrons) · Standard · Paper 2 style · 5 marks
(a)Show that the K⁰ meson, with quark composition d s̄, has zero charge.[1]
(b)State the quark composition of the antiparticle of the K⁰.[1]
(c)Explain how a neutral particle such as the K⁰ can have an antiparticle that is a different particle from itself.[2]
(d)State whether the K⁰ is a hadron or a lepton, and give a reason.[1]
Show answer
(a) −⅓ + ⅓ = 0
B1
(b) s d̄
B1
(c) Its antiparticle is made of the antiquarks of its quarks (s d̄ instead of d s̄); the quark content is different even though both charges are zero.
B1 antiparticle has each quark replaced by its antiquark; B1 d s̄ ≠ s d̄, so they are different particles
(d) A hadron (a meson), because it is made of quarks.
B1
Q27Fundamental particles (quarks, leptons, hadrons) · Challenge · Paper 1 style · 1 mark
(a)[1]
Show answer
(a) A u → d + e⁺ + ν
Proton uud → neutron udd, so an up quark becomes a down quark; charge +⅔ = −⅓ + 1 needs a positron, and β⁺ decay emits an electron neutrino (not an antineutrino). D is β⁻ decay.
Q28Fundamental particles (quarks, leptons, hadrons) · Challenge · Paper 2 style · 6 marks
(a)The Δ⁺⁺ baryon contains three quarks, all of the same flavour. Determine its quark composition.[1]
(b)Explain why no meson can have a charge of +2e.[2]
(c)State the possible charges, in terms of e, of a meson.[1]
(d)A student claims that a baryon of charge +e could be made of two up quarks and one strange antiquark. Explain why the student is wrong.[2]
Show answer
(a) u u u
B1 3 × ⅔ = +2
(b) A meson is one quark and one antiquark; the largest possible charge is +⅔ + ⅓ = +1 (e.g. u d̄), so +2e is impossible.
(d) u u s̄ has charge +⅔ + ⅔ + ⅓ = +5/3, which is not a whole number; also a baryon must be three quarks or three antiquarks, not a mixture.
B1 charge would be +5/3 e; B1 baryons are qqq or q̄q̄q̄, not a mixture
Q29Fundamental particles (quarks, leptons, hadrons) · Challenge · Paper 2 style · 6 marks
Quarks come in six flavours: up (u), down (d), strange (s), charm (c), top (t) and bottom (b). The charm quark has charge +⅔e and the bottom quark has charge −⅓e.
(a)Determine, in terms of e, the charge of each meson: (i) D⁰ (c ū), (ii) D_s⁺ (c s̄), (iii) B⁻ (b ū), (iv) B⁺ (u b̄).[4]
(b)State the quark composition of the antiparticle of the D_s⁺ meson and give its charge.[2]
