Particle Physics: Physics 9702 (Cambridge International AS & A Level)

A newly catalogued radioactive sample contains atoms of a nuclide with 18 protons and 22 neutrons in each nucleus. The element is temporarily labelled X.

Which nuclide notation correctly represents this nuclide?

A student is checking whether the following equation correctly represents $\beta^-$ decay at the level of an individual quark inside a nucleus:

$u \rightarrow d + e^{-} + \bar\nu_e$

The electron and the antineutrino are correctly identified as the pair of leptons released in $\beta^-$ decay, but the equation as a whole does not correctly represent the decay.

Which physical quantity is not conserved by this equation, as written?

In an experiment based on the original alpha-particle scattering investigation, a narrow beam of $\alpha$-particles is directed at a thin sheet of gold foil in an evacuated chamber. A detector that can be rotated around the foil counts the number of $\alpha$-particles scattered through different angles.

Three key observations are made:

• Observation 1: the great majority of $\alpha$-particles pass straight through the foil with little or no deflection.
• Observation 2: a small fraction of the $\alpha$-particles are deflected through large angles, some greater than $90°$.
• Observation 3: a very small fraction of the $\alpha$-particles are deflected back through angles close to $180°$, almost directly back towards the source.

(a) State the nuclear model of the atom that these observations led scientists to propose. [2]

(b) Explain what Observation 1 shows about the structure of a gold atom. [2]

(c) Explain what Observations 2 and 3 show about the nucleus of a gold atom, referring to both its size and its charge. [3]

A geology student is using a mass spectrometer to study a rock sample that contains three different nuclides, used for radiometric dating.

• Nuclide 1 has a nucleon number of 40 and a proton number of 19.
• Nuclide 2 has the same proton number as Nuclide 1, but a nucleon number of 39.
• Nuclide 3 has a proton number of 20 and a nucleon number of 40.

(a) Write the nuclide notation for Nuclide 1 and for Nuclide 2, using X to represent the (unnamed) element. [2]

(b) Determine the number of neutrons in the nucleus of Nuclide 1 and in the nucleus of Nuclide 2. [2]

(c) State what makes Nuclide 1 and Nuclide 2 isotopes of the same element. [1]

(d) State, with a reason, whether Nuclide 3 is also an isotope of the same element as Nuclide 1 and Nuclide 2. [2]

A sample of the radioisotope sodium-24, $^{24}_{11}\text{Na}$, is used to trace the flow of fluid through an industrial pipeline. This nuclide is unstable and decays by $\beta^-$ emission to form a nuclide of magnesium, Mg.

(a) Write a balanced nuclide equation for this $\beta^-$ decay. Include the correct symbol for the emitted beta particle and the correct type of neutrino or antineutrino. [3]

(b) State the proton number and the nucleon number of the daughter nuclide of magnesium formed, and show that both charge and nucleon number are conserved in your equation from (a). [3]

(c) One neutron inside the sodium-24 nucleus is transformed during this decay. Write the equation for this change at the level of the individual quarks involved, and show that electric charge is conserved in this quark-level equation. [4]

A newly detected baryon is found to have the quark composition $uds$, one up quark, one down quark and one strange quark.

Using quark charges of $+\frac23e$ for the up quark and $-\frac13e$ for both the down quark and the strange quark, what is the total charge of this baryon?

A physics teacher lists five particles on the board for a classification exercise: a proton, an electron, a neutron, a $\pi^+$ meson (quark composition $u\bar{d}$, i.e. an up quark bound to a down antiquark), and a muon-neutrino.

(a) State which of these five particles are leptons and which are hadrons. Give a reason for your classification, based on whether each type of particle has an internal quark composition. [2]

(b) Among the hadrons identified in (a), state which are baryons and which are mesons. Give a reason for your classification, based on the number and type of quarks each contains. [3]

(c) State one similarity and one difference between the electron and the proton, in terms of their internal structure. [2]

A $\pi^+$ meson has the quark composition $u\bar{d}$, an up quark bound to a down antiquark.

Given that the up quark has charge $+\frac23e$ and the down quark has charge $-\frac13e$ (so the down antiquark has charge $+\frac13e$), what is the total charge of the $\pi^+$ meson?

A particle physicist is studying a newly produced baryon, provisionally named Particle Y. Detector measurements show that Particle Y has a total charge of $+1e$, and further analysis confirms it contains two up quarks and one strange quark (composition $uus$).

(a) Using $+\frac23e$ for the up quark charge and $-\frac13e$ for the strange quark charge, show that this composition is consistent with the measured total charge of $+1e$. [2]

(b) State why Particle Y is classified as a baryon rather than a meson. [1]

(c) The proton also has a total charge of $+1e$ and is composed of two up quarks and one down quark ($uud$). Explain why Particle Y is not simply a proton, even though both particles are made of "two up quarks and one other quark" with the same total charge. [3]

The antiproton, $\bar{p}$, is the antiparticle of the proton. The proton has quark composition $uud$, with quark charges $+\frac23e$ for the up quark and $-\frac13e$ for the down quark.

(a) State the general relationship between the mass of any particle and the mass of its corresponding antiparticle, and the general relationship between their charges. [2]

(b) State the composition of the antiproton in terms of antiquarks. [1]

(c) Given that each antiquark carries the exact opposite charge to its corresponding quark, calculate the total charge of the antiproton. Show that this result is consistent with your answer to (a). [3]

(d) The antiproton is built from three antiquarks rather than a quark-antiquark pair. State, with a reason, whether this places the antiproton in the same family of hadrons as the proton (baryons) or in the family of mesons. [2]