Exploring the Structure of Matter (Edexcel A Level Physics): Exam Questions

The diagram shows a model used to demonstrate alpha particle scattering. A ball bearing is set rolling on a wooden track. The track is positioned so that the ball bearing rolls onto a metal sheet with a curved surface known as a ʻhillʼ.

The diagram shows a vertical cross-section through the hill. The surface is curved so that the height of a point h on the curved surface is inversely proportional to the distance r from the centre of the hill.

Explain why the hill is suitable as a model for the electric field surrounding the nucleus of an atom.

A plan view of the arrangement is shown.

The wooden track is moved to different positions and the ball bearing is released.

Describe the results of the alpha particle scattering experiment and how these can be demonstrated by moving the wooden track to different positions.

At the beginning of the 20th century, Rutherford carried out large-angle alpha particle scattering experiments using gold (${}_{79}{}^{197}\mathrm{Au}$) foil.

The vast majority of the alpha particles went straight through the foil whilst a few were deflected straight back.

Describe how the model of the atom changed, as a consequence of these experiments.

In one experiment the alpha particles had an initial energy of 7.7 MeV.

Calculate the distance of closest approach of the alpha particles to the nucleus of a gold atom. Assume that the gold nucleus remains at rest.

Distance of closest approach = ............................................

Rutherford also carried out the experiment with aluminium (${}_{13}{}^{27}\mathrm{Al}$) foil.

The aluminium foil had the same thickness as the gold foil and the alpha particles had the same initial kinetic energy.

The following observations were made.

Observation 1:

The fraction of alpha particles scattered at any particular angle for aluminium foil was always much less than for gold foil.

Observation 2:

The alpha particles scattered from aluminium foil had less kinetic energy than the alpha particles scattered from gold foil.

Explain how these observations can be used to deduce how an aluminium nucleus compares to a gold nucleus.

The bubble chamber photograph shows tracks made by a proton and a pion. The proton and pion were both created by the decay of a lambda particle. No other particles were produced.

Explain how observations and measurements from the photograph can be used to establish information about the lambda particle.

The lambda particle consists of up, down and strange quarks.

Explain how the conservation of charge, baryon number and lepton number apply to the decay of the lambda particle.

Write an equation to represent the decay of the lambda (Λ) particle.

The rest mass of the lambda particle is $1115\text{ MeV}/c^2$.

(i) Calculate this mass in kg.

Mass = ....................................................... kg

[3]

(ii) The rest mass of a proton is $940\text{ MeV}/c^2$. The rest mass of a pion is $140\text{ MeV}/c^2$.

The kinetic energy of the lambda particle just before decay is 4.95 GeV.

Calculate the total kinetic energy of the proton and pion in MeV.

Total kinetic energy = ....................................................... MeV

[3]

The discovery of the Higgs particle was an important contribution to our understanding of particle physics.

Describe the standard model for subatomic particles. You should identify the fundamental particles and the composition of the particles we can observe.

The mass of the Higgs particle is 2.2× 10^–25 kg.

Calculate this mass in GeV/c²

Mass = ........................................... GeV/c²

The Higgs particle was discovered using the Large Hadron Collider (LHC) in 2012.

Two beams of very high energy protons, moving in opposite directions, were made to collide.

i) Explain the need for such high energy collisions.

(3)

ii) The beams of protons are contained within a ring of superconducting magnets.

Calculate the momentum of a proton in a beam.

magnetic field strength = 8.3 T

circumference of the ring = 27 km

Momentum = ........................................(3)

iii) State the total momentum of the products of the collision between the two beams of protons.

Total momentum = .....................................(1)

The LHC accelerates protons until they gain energies of about 7 TeV.

A student used the equation $E_k=\frac{p^2}{2m}$ to predict the energy of a proton in the beam, using the momentum calculated in (c)(ii), but found the energy was far higher than 7 TeV.

Explain why.

A muon (μ) is a lepton with a mass of 106 MeV / c².

Calculate the mass of a muon in kg.  

                                 Mass of muon = ...................................kg

Muons are produced from the decay of pions in the upper atmosphere.

An example of this decay is given by the equation

${\mathrm{\pi }}^{-}\to {\mathrm{\mu }}^{-}+{\overline{\mathrm{v}}}_{\mathrm{\mu }}$

i) Explain how this decay obeys the laws of conservation of charge, baryon number and lepton number. 

(3)

ii) The masses of these three particles, in MeV/c², are given below. 

Explain why the total kinetic energy of the products of this decay is approximately 34 MeV. Assume the ${\mathrm{\pi }}^{-}$ stationary. 

(2)

iii) State which two conservation laws could be used to calculate the kinetic energy of the ${\mathrm{\mu }}^{-}$ and the ${\overline{v}}_{\mu }$, just after the decay of the ${\mathrm{\pi }}^{-}$.  

(2)

iv) The muons are produced at a height of 10 km in the atmosphere. The velocity of the muons is 0.99 c. The average lifetime for muons is normally 2.2 μs and yet muons produced in the upper atmosphere are found in significant numbers at sea level.

Discuss this apparent anomaly. 

(6)

The ${\mathrm{\pi }}^{-}$ particle is a meson of mass $139.57{\text{ MeV/c}}^2$. It decays via the weak interaction, producing a muon and a neutrino.

The table shows the properties of two quarks.

(i) Give the quark structure of a ${\mathrm{\pi }}^{-}$ particle.

[1]

(ii) Complete the particle equation for this decay.

${\mathrm{\pi }}^{-}\to$

[2]

Energy and momentum must be conserved in this decay.

Explain how two other conservation laws apply to this decay.

Calculate the mass, in kg, of the ${\mathrm{\pi }}^{-}$ particle.

Pions are produced in the upper atmosphere when cosmic rays, consisting mainly of high-energy protons, collide with nuclei.

Explain why a single cosmic ray could lead to the creation of several pions.

The muons produced from the decay of these pions travel towards the Earth's surface at a velocity of $0.99 c$. The average lifetime for muons at rest is $2.2\times {10}^{-6}\text{ s}$, yet muons produced at a height of $10\text{ km}$ are found in significant numbers at sea level.

Explain whether this observation is consistent with ideas from relativity. Your answer should include a calculation.

A hospital radiotherapy unit uses a linear accelerator (linac) to produce beams of high-energy electrons.

The diagram shows the initial section of a linac. The electron source is a metal disc.

Describe how a metal disc can be made to emit electrons.

Each electron leaves the linac with a kinetic energy of $8.0\times {10}^{-12}\text{ J}$.

Calculate the total potential difference through which each electron is accelerated.

Explain how the linac produces a beam of high-energy electrons.

The diagram shows the structure of a cyclotron.

A uniform magnetic field is applied perpendicular to the plane of the dees. An alternating potential difference is applied across the gap between the dees.

Explain how the cyclotron produces a beam of high-energy protons.

The frequency of the alternating potential difference is constant.

Derive an expression to show that the time taken by a proton to travel around one dee is independent of the radius of its path.

The dees of the cyclotron have a radius of $0.60\text{m}$.

Calculate the maximum speed of a proton as it leaves the cyclotron.

magnetic flux density = $0.80\text{T}$

The protons strike a stationary target at X inside a bubble chamber. The diagram shows the tracks produced by one collision. Two neutral particles are produced in the collision, and both later decay into charged particles. A uniform magnetic field is applied perpendicular to the plane of the diagram.

Explain the evidence provided by the diagram for these particle interactions.