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PHYSICS, M8 2024 HSC 23

Development of models of the atom has resulted from both experimental investigations and hypotheses based on theoretical considerations.

  1. A key piece of experimental evidence supporting the nuclear model of the atom was a discovery by Chadwick in 1932.
  2. An aspect of the experimental design is shown.
     

    1. What was the role of paraffin in Chadwick's experiment?   (2 marks)

    2. How did Chadwick's experiment change the model of the atom?  (3 marks)

  2. Explain how de Broglie's hypothesis regarding the nature of electrons addressed limitations in the Bohr-Rutherford model of the atom.   (4 marks)

Show Answers Only

a.i.  Role of paraffin wax:

  • Paraffin wax is a rich source of protons.
  • When the paraffin was placed in front of the unknown radiation, the transfer of momentum from the radiation caused protons to be emitted from the paraffin wax.
  • The emitted protons could then be detected and analysed.
  • From studying the protons ejected from the paraffin wax, Chadwick proposed the existence of the neutron.
     

a.ii. Changes to the model of the atom:

  • Previous to Chadwick’s experiment, the model of the atom proposed by Rutherford consisted of a dense positive charge in the nucleus which was orbited by electrons.
  • In this model however, the protons did not account for the total mass of the nucleus.
  • Through using the conservation of momentum and energy in his experiment, Chadwick proposed the existence of the neutron particle which was slightly heavier than the proton.
  • The model of the atom was updated to include both protons and neutrons in the nucleus which then fully accounted for the mass of the nucleus.
     

b.   Limitations in the Bohr-Rutherford model:

  • Rutherford’s model of the atom stated that electrons orbited the nucleus and were electrostatically attracted to the positive nucleus. This meant that the electrons were in circular motion and were constantly under centripetal acceleration.
  • However, Maxwell predicted that an accelerating charge would emit electro-magnetic radiation and in Rutherford’s model, all atoms should have been unstable as the electrons would emit EMR, lose energy and spiral into the nucleus.
  • Bohr proposed that electrons orbited the nucleus in stationary states at fixed energies with no intermediate states possible where they would not emit EMR but provided no theoretical explanation for this.

De Broglie’s hypothesis:

  • De Broglie proposed that electrons could exhibit a wave nature and could act as matter-waves. The electrons would form standing waves around the nucleus and would no longer be an accelerating particle which addressed the limitation of all atoms being unstable.
  • Further, De Broglie proposed that the standing waves would occur at integer wavelengths where the circumference of the electron orbit would be equal to an integer electron wavelength, \(2\pi r=n\lambda\)  where  \(\lambda = \dfrac{h}{mv}\). At any other radii other than this, deconstructive interference would occur and a standing electron wave would not form. This addressed why electrons could only be present at fixed radii/energy levels in the atom.

Show Worked Solution

a.i.  Role of paraffin wax:

  • Paraffin wax is a rich source of protons.
  • When the paraffin was placed in front of the unknown radiation, the transfer of momentum from the radiation caused protons to be emitted from the paraffin wax.
  • The emitted protons could then be detected and analysed.
  • From studying the protons ejected from the paraffin wax, Chadwick proposed the existence of the neutron. 
Mean mark (a)(i) 52%.

a.ii. Changes to the model of the atom:

  • Previous to Chadwick’s experiment, the model of the atom proposed by Rutherford consisted of a dense positive charge in the nucleus which was orbited by electrons.
  • In this model however, the protons did not account for the total mass of the nucleus.
  • Through using the conservation of momentum and energy in his experiment, Chadwick proposed the existence of the neutron particle which was slightly heavier than the proton.
  • The model of the atom was updated to include both protons and neutrons in the nucleus which then fully accounted for the mass of the nucleus. 

b.   Limitations in the Bohr-Rutherford model:

  • Rutherford’s model of the atom stated that electrons orbited the nucleus and were electrostatically attracted to the positive nucleus. This meant that the electrons were in circular motion and were constantly under centripetal acceleration.
  • However, Maxwell predicted that an accelerating charge would emit electro-magnetic radiation and in Rutherford’s model, all atoms should have been unstable as the electrons would emit EMR, lose energy and spiral into the nucleus.
  • Bohr proposed that electrons orbited the nucleus in stationary states at fixed energies with no intermediate states possible where they would not emit EMR but provided no theoretical explanation for this.

De Broglie’s hypothesis:

  • De Broglie proposed that electrons could exhibit a wave nature and could act as matter-waves. The electrons would form standing waves around the nucleus and would no longer be an accelerating particle which addressed the limitation of all atoms being unstable.
  • Further, De Broglie proposed that the standing waves would occur at integer wavelengths where the circumference of the electron orbit would be equal to an integer electron wavelength, \(2\pi r=n\lambda\)  where  \(\lambda = \dfrac{h}{mv}\). At any other radii other than this, deconstructive interference would occur and a standing electron wave would not form. This addressed why electrons could only be present at fixed radii/energy levels in the atom.
♦ Mean mark (b) 44%.

PHYSICS, M8 2023 HSC 33

Consider the following statement.

The interaction of subatomic particles with fields, as well as with other types of particles and matter, has increased our understanding of processes that occur in the physical world and of the properties of the subatomic particles themselves.

Justify this statement with reference to observations that have been made and experiments that scientists have carried out.   (9 marks)

Show Answers Only

Thomson’s Experiment:

  • Thomson’s experiment tested the interaction of cathode rays (which he discovered were negatively charged subatomic particles and named them electrons) with electric and magnetic fields to determine the charge to mass ratio (\(\dfrac{q}{m}\)) of the electrons.
  • Using both the electric and magnetic fields, Thomson balanced the forces to ensure the cathode rays travelled through undeflected. Thus:
  •    \(F_E = F_B \ \ \Rightarrow \ \ qE=qvB \ \ \Rightarrow \ \ v=\dfrac{E}{B}\)
  • Using the magnetic field and known velocity, the cathode rays travelled in a circular path due to their negative charges interacting with the magnetic field. Thus:
  •    \(F_c=F_B\ \ \Rightarrow \ \ \dfrac{mv^2}{r}=qvB \ \ \Rightarrow \ \ \dfrac{q}{m}=\dfrac{v}{Br}\)
  • The charge to mass ratio was determined to be 0.77 \(\times\) 10\(^{11}\) Ckg\(^{-1}\) and was \(\dfrac{1}{1800}\) times smaller than the charge to mass ratio of the proton. The number was also the same regardless of the metal cathode used, thus Thomson determined this particle was a fundamental constitute of all matter. 
  • Therefore, the statement is true as the observations and experiment undertaken by Thomson using the interactions of particles and fields led to a greater understanding of the electrons. 

Chadwick’s Experiment:

  • In Chadwick’s experiment, he irradiated beryllium with alpha particles which emitted a deeply penetrating radiation with neutral charge. When this particle was directed into paraffin wax, protons were emitted and detected on a screen. 
  • Using the Laws of conservation of energy and momentum, Chadwick proposed the idea of a neutral particle and named it the neutron. He determined that the mass of this particle must be slightly greater than the mass of the proton.
  • Therefore, Chadwick’s observations of the neutrons led to a greater understanding of the properties of the particle, thus justifying the statement above.  

Observations using particle accelerators:

  • Particle accelerators have led to many new scientific discoveries as a result of the interaction of particles with fields and particle-particle interactions.
  • Scientists have come to a greater understanding of quarks and other subatomic particles within the standard model of matter and processes of the physical world including decay trails and momentum dilation.
  • The Large Hadron Collider (LHC) can accelerate particles close to the speed of light using electric and magnetic fields. When particles collide, the kinetic energy is converted into mass using Einstein’s equation  \(E=mc^2\).
  • The new particles formed as a result of these collisions led to the development of the standard model and increased scientific understanding of subatomic particles including up and down quarks, W/Z bosons and the Higgs Boson.
  • These subatomic particles have very short lifetimes before decaying into more stable particles. Our knowledge of them is primarily from studying their decay properties which has led to a greater understanding of particle decay trails.
  • Observations of interactions within particles accelerators has also increased the scientific understanding of momentum dilation. As particles reach relativistic speeds, a greater force is required to accelerate them than classical physics predicts which is due to mass and momentum dilation. 

Other Answers could include:

  • Millikan’s Oil drop experiment.
  • The photoelectric effect.
  • Geiger Marsden experiment.
  • Davisson Germer experiment.
  • Observations of Muons.
Show Worked Solution

One (of many) exemplar responses.

Thomson’s Experiment:

  • Thomson’s experiment tested the interaction of cathode rays (which he discovered were negatively charged subatomic particles and named them electrons) with electric and magnetic fields to determine the charge to mass ratio (\(\dfrac{q}{m}\)) of the electrons.
  • Using both the electric and magnetic fields, Thomson balanced the forces to ensure the cathode rays travelled through undeflected. Thus:
  •    \(F_E = F_B \ \ \Rightarrow \ \ qE=qvB \ \ \Rightarrow \ \ v=\dfrac{E}{B}\)
  • Using the magnetic field and known velocity, the cathode rays travelled in a circular path due to their negative charges interacting with the magnetic field. Thus:
  •    \(F_c=F_B\ \ \Rightarrow \ \ \dfrac{mv^2}{r}=qvB \ \ \Rightarrow \ \ \dfrac{q}{m}=\dfrac{v}{Br}\)
  • The charge to mass ratio was determined to be 0.77 \(\times\) 10\(^{11}\) Ckg\(^{-1}\) and was \(\dfrac{1}{1800}\) times smaller than the charge to mass ratio of the proton. The number was also the same regardless of the metal cathode used, thus Thomson determined this particle was a fundamental constitute of all matter. 
  • Therefore, the statement is true as the observations and experiment undertaken by Thomson using the interactions of particles and fields led to a greater understanding of the electrons.

Chadwick’s Experiment:

  • In Chadwick’s experiment, he irradiated beryllium with alpha particles which emitted a deeply penetrating radiation with neutral charge. When this particle was directed into paraffin wax, protons were emitted and detected on a screen. 
  • Using the Laws of conservation of energy and momentum, Chadwick proposed the idea of a neutral particle and named it the neutron. He determined that the mass of this particle must be slightly greater than the mass of the proton.
  • Therefore, Chadwick’s observations of the neutrons led to a greater understanding of the properties of the particle, thus justifying the statement above.  

Observations using particle accelerators:

  • Particle accelerators have led to many new scientific discoveries as a result of the interaction of particles with fields and particle-particle interactions.
  • Scientists have come to a greater understanding of quarks and other subatomic particles within the standard model of matter and processes of the physical world including decay trails and momentum dilation.
  • The Large Hadron Collider (LHC) can accelerate particles close to the speed of light using electric and magnetic fields. When particles collide, the kinetic energy is converted into mass using Einstein’s equation  \(E=mc^2\).
  • The new particles formed as a result of these collisions led to the development of the standard model and increased scientific understanding of subatomic particles including up and down quarks, W/Z bosons and the Higgs Boson.
  • These subatomic particles have very short lifetimes before decaying into more stable particles. Our knowledge of them is primarily from studying their decay properties which has led to a greater understanding of particle decay trails.
  • Observations of interactions within particles accelerators has also increased the scientific understanding of momentum dilation. As particles reach relativistic speeds, a greater force is required to accelerate them than classical physics predicts which is due to mass and momentum dilation. 

Other Answers could include:

  • Millikan’s Oil drop experiment.
  • The photoelectric effect.
  • Geiger Marsden experiment.
  • Davisson Germer experiment.
  • Observations of Muons.
♦♦ Mean mark 45%.

PHYSICS, M8 2018 HSC 34bi

The diagram shows apparatus used to investigate subatomic particles.
 

     

How did Chadwick use a law of physics to identify a property of `X`?   (2 marks)

Show Answers Only
  • Chadwick measured the momentum of both `X` and the ejected protons.
  • Using the law of conservation of momentum he was able to calculate the mass of `X` which was similar to the mass of a proton.
Show Worked Solution
  • Chadwick measured the momentum of both `X` and the ejected protons.
  • Using the law of conservation of momentum he was able to calculate the mass of `X` which was similar to the mass of a proton.

PHYSICS, M8 2020 HSC 29

In an experiment, alpha particles were fired into a thin sheet of beryllium. Unknown radiation was detected.
 

Further experiments were conducted in which it was observed that the unknown radiation:

    • was not deflected by an electric field
    • caused protons to be ejected from a block of paraffin
    • could not produce the photoelectric effect.

Scientists debated the nature of this unknown radiation, hypothesising that it was gamma radiation.

  1. Explain why the hypothesis was proposed and then rejected, with reference to the observations.   (3 marks)
  1. How did these experiments change the model of the atom?   (2 marks)
Show Answers Only

a.    Hypothesis proposal and subsequent rejection:

  • The unknown radiation was not deflected by an electric field which is consistent with the properties of gamma radiation which is electrically neutral. This observation supported the hypothesis.
  • However, the hypothesis was rejected as the unknown radiation was able to eject protons from paraffin indicating it carried significant momentum. This was inconsistent with the radiation being gamma radiation.
  • Additionally, the unknown radiation was unable to produce the photoelectric effect. This was also inconsistent with the unknown radiation being gamma radiation as the high photon energy of gamma rays would readily eject photoelectrons from a metal. 

b.    Changes to the model of the atom:

  • These experiments were used to demonstrate the existence of neutrons, a neutral particle with mass similar to protons.
  • This changed the model of the atom as the atomic nucleus was represented as containing protons and neutrons rather than just protons.
Show Worked Solution

a.    Hypothesis proposal and subsequent rejection:

  • The unknown radiation was not deflected by an electric field which is consistent with the properties of gamma radiation which is electrically neutral. This observation supported the hypothesis.
  • However, the hypothesis was rejected as the unknown radiation was able to eject protons from paraffin indicating it carried significant momentum. This was inconsistent with the radiation being gamma radiation.
  • Additionally, the unknown radiation was unable to produce the photoelectric effect. This was also inconsistent with the unknown radiation being gamma radiation as the high photon energy of gamma rays would readily eject photoelectrons from a metal. 

b.    Changes to the model of the atom:

  • These experiments were used to demonstrate the existence of neutrons, a neutral particle with mass similar to protons.
  • This changed the model of the atom as the atomic nucleus was represented as containing protons and neutrons rather than just protons.