smc-3701-40-Rutherford

PHYSICS, M8 2024 HSC 23

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

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

1. What was the role of paraffin in Chadwick's experiment? (2 marks)
  
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2. How did Chadwick's experiment change the model of the atom? (3 marks)
  
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Explain how de Broglie's hypothesis regarding the nature of electrons addressed limitations in the Bohr-Rutherford model of the atom. (4 marks)

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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 EQ-Bank 26

Observations and mathematical ideas are critical to the improvement of scientific models.

Discuss this statement with reference to scientific discoveries that have contributed to our understanding of the atom. (8 marks)

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[P] Observations have been critical in advancing atomic models.
[E] When experiments reveal unexpected results, scientists must revise their models to match reality.
[Ev] The Geiger-Marsden experiment showed alpha particles bouncing back from gold foil, contradicting the plum pudding model. This led Rutherford to propose a dense nucleus.
[L] This demonstrates how observations drive scientific progress in understanding atoms.
[P] Mathematical ideas provide essential frameworks for atomic models.
[E] Mathematics allows scientists to make precise predictions and test theories quantitatively.
[Ev] Bohr developed a mathematical model explaining the specific wavelengths emitted which relies on Rydberg’s equation: `(1)/(lambda)=R((1)/(n_(f)^2)-(1)/(n_(i)^2))`.
[Ev] This model was limited as it was only able to explain the hydrogen atom. De Broglie built upon it by postulating that electrons behaved as a wave, eventually describing the equation `\lambda=h/{mv}` which helped explain electron wave behaviour.
[L] These mathematical models transformed vague ideas into testable predictions about atomic structure.
[P] However, observations and mathematics alone have limitations.
[E] Models based purely on observations can miss underlying principles without theoretical insight.
[Ev] Bohr’s model perfectly matched hydrogen spectra but failed for other atoms because it lacked deeper quantum understanding.
[L] This shows that observation and mathematics need theoretical frameworks to truly advance atomic understanding.
[P] Nevertheless, observations and mathematical ideas remain fundamental to atomic theory development.
[E] Despite limitations, these tools work together to progressively refine scientific understanding.
[Ev] The progression from Rutherford to Bohr to de Broglie shows each model building on previous observations and mathematical frameworks, creating increasingly accurate atomic models.
[L] Therefore, the statement is valid as both elements are critical for advancing our understanding of the atom.

Answers could also reference:

Thomson’s discovery of the electron.
Further contributions from Davisson-Germer as well as Schrodinger and Heisenberg.

Show Worked Solution

[P] Observations have been critical in advancing atomic models.
[E] When experiments reveal unexpected results, scientists must revise their models to match reality.
[Ev] The Geiger-Marsden experiment showed alpha particles bouncing back from gold foil, contradicting the plum pudding model. This led Rutherford to propose a dense nucleus.
[L] This demonstrates how observations drive scientific progress in understanding atoms.
[P] Mathematical ideas provide essential frameworks for atomic models.
[E] Mathematics allows scientists to make precise predictions and test theories quantitatively.
[Ev] Bohr developed a mathematical model explaining the specific wavelengths emitted which relies on Rydberg’s equation: `(1)/(lambda)=R((1)/(n_(f)^2)-(1)/(n_(i)^2))`.
[Ev] This model was limited as it was only able to explain the hydrogen atom. De Broglie built upon it by postulating that electrons behaved as a wave, eventually describing the equation `\lambda=h/{mv}` which helped explain electron wave behaviour.
[L] These mathematical models transformed vague ideas into testable predictions about atomic structure.
[P] However, observations and mathematics alone have limitations.
[E] Models based purely on observations can miss underlying principles without theoretical insight.
[Ev] Bohr’s model perfectly matched hydrogen spectra but failed for other atoms because it lacked deeper quantum understanding.
[L] This shows that observation and mathematics need theoretical frameworks to truly advance atomic understanding.
[P] Nevertheless, observations and mathematical ideas remain fundamental to atomic theory development.
[E] Despite limitations, these tools work together to progressively refine scientific understanding.
[Ev] The progression from Rutherford to Bohr to de Broglie shows each model building on previous observations and mathematical frameworks, creating increasingly accurate atomic models.
[L] Therefore, the statement is valid as both elements are critical for advancing our understanding of the atom.

Answers could also reference:

Thomson’s discovery of the electron.
Further contributions from Davisson-Germer as well as Schrodinger and Heisenberg.

PHYSICS M8 2022 HSC 31

Following the Geiger-Marsden experiment, Rutherford proposed a model of the atom.

Bohr modified this model to explain the spectrum of hydrogen observed in experiments.

The Bohr-Rutherford model of the atom consists of electrons in energy levels around a positive nucleus.

How do features of this model account for all the experimental evidence above? Support your answer with a sample calculation and a diagram, and refer to energy, forces and photons. (9 marks)

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The Geiger-Marsden experiment, which involved firing alpha particles at a thin sheet of gold foil produced results which can be explained by the Bohr-Rutherford model:

The majority of fired alpha particles passed through the gold foil undeflected. Rutherford concluded from this that the atom had a small, central nucleus.
Some alpha particles were deflected and some of these were deflected at very large angles. Rutherford concluded from this that the nucleus was dense and positively charged exerting a repulsive electromagnetic force on the fired alpha particles.
The model accounts for Rutherford’s conclusions, placing electrons in orbits around a small positive nucleus.

Rutherford’s model alone could not explain the emission spectra of elements such as hydrogen. Bohr’s contribution to the Bohr-Rutherford model amended this:

Bohr proposed that electrons orbited the atomic nucleus in quantised orbits at fixed energies. He proposed that electrons could move from a higher energy orbit (eg. n=1) to a lower energy orbit (n=3) by emitting a photon with energy `E=hf` equal to the energy difference between the two orbits.
Additionally, he proposed that electrons could move from a lower energy orbit to a higher energy orbit by absorbing a photon with energy `E=hf` equal to the energy difference between the two orbits.
This is able to account for the given emission spectra of hydrogen, where emission lines correspond to electron transitions from higher energy orbits to the second energy orbit which produce photons within the spectrum of visible light.

Using Rydberg’s equation it is possible to predict the emission lines of hydrogen, using an electron moving from the sixth to the second Bohr energy orbit as an example:

`(1)/(lambda)`	`=R((1)/(n_(f)^(2))-(1)/(n_(i)^(2)))`
	`=(1.097 xx10^7)((1)/(2^(2))-(1)/(6^(2)))`
	`=(2 xx1.097 xx10^7)/(9)`
	`=2.438 xx10^6`
`lambda`	`=410 text{nm}`

This value corresponds to the leftmost line on the given spectrum, reflecting how Bohr’s model can account for the emission spectra of hydrogen.

Show Worked Solution

The Geiger-Marsden experiment, which involved firing alpha particles at a thin sheet of gold foil produced results which can be explained by the Bohr-Rutherford model:

The majority of fired alpha particles passed through the gold foil undeflected. Rutherford concluded from this that the atom had a small, central nucleus.
Some alpha particles were deflected and some of these were deflected at very large angles. Rutherford concluded from this that the nucleus was dense and positively charged exerting a repulsive electromagnetic force on the fired alpha particles.
The model accounts for Rutherford’s conclusions, placing electrons in orbits around a small positive nucleus.

Rutherford’s model alone could not explain the emission spectra of elements such as hydrogen. Bohr’s contribution to the Bohr-Rutherford model amended this:

Bohr proposed that electrons orbited the atomic nucleus in quantised orbits at fixed energies. He proposed that electrons could move from a higher energy orbit (eg. n=1) to a lower energy orbit (n=3) by emitting a photon with energy `E=hf` equal to the energy difference between the two orbits.
Additionally, he proposed that electrons could move from a lower energy orbit to a higher energy orbit by absorbing a photon with energy `E=hf` equal to the energy difference between the two orbits.
This is able to account for the given emission spectra of hydrogen, where emission lines correspond to electron transitions from higher energy orbits to the second energy orbit which produce photons within the spectrum of visible light.

Using Rydberg’s equation it is possible to predict the emission lines of hydrogen, using an electron moving from the sixth to the second Bohr energy orbit as an example:

`(1)/(lambda)`	`=R((1)/(n_(f)^(2))-(1)/(n_(i)^(2)))`
	`=(1.097 xx10^7)((1)/(2^(2))-(1)/(6^(2)))`
	`=(2 xx1.097 xx10^7)/(9)`
	`=2.438 xx10^6`
`lambda`	`=410 text{nm}`

This value corresponds to the leftmost line on the given spectrum, reflecting how Bohr’s model can account for the emission spectra of hydrogen.

♦ Mean mark 51%.

PHYSICS, M8 2019 HSC 3 MC

Geiger and Marsden carried out an experiment to investigate the structure of the atom.

Which diagram identifies the particles they used and the result that they INITIALLY expected?

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`C`

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They used alpha particles. Based on Thomson’s model it was initially expected that all alpha particles would pass through the atom.

`=>C`