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PHYSICS, M8 2019 VCE 17

Students are comparing the diffraction patterns produced by electrons and X-rays, in which the same spacing of bands is observed in the patterns, as shown schematically in Figure 18. Note that both patterns shown are to the same scale.
 

The electron diffraction pattern is produced by 3.0 × 10\(^3\) eV electrons.

  1. Explain why electrons can produce the same spacing of bands in a diffraction pattern as X-rays.  (3 marks)
  1. Calculate the frequency of X-rays that would produce the same spacing of bands in a diffraction pattern as for the electrons. Show your working.  (4 marks)
Show Answers Only

a.    → Electrons with momentum exhibit wave-like properties.

→  In this way, moving electrons produce a de Broglie wavelength.

→  As diffraction is a wave phenomenon and is dependent on wavelengths, if the de Broglie wavelength of an electron matches the wavelength of an X-ray then spacing of the bands will be the same.
 

b.    \(1.34 \times 10^{19}\ \text{Hz}\)

Show Worked Solution

a.    → Electrons with momentum exhibit wave-like properties.

→  In this way, moving electrons produce a de Broglie wavelength.

→  As diffraction is a wave phenomenon and is dependent on wavelengths, if the de Broglie wavelength of an electron matches the wavelength of an X-ray then spacing of the bands will be the same.
 

♦ Mean mark (a) 49%.

b.    Find velocity of the electrons using  \(E=\dfrac{1}{2}mv^2 :\)

\(3.0 \times 10^3 \times 1.602 \times 10^{-19}=\dfrac{1}{2} \times 9.109 \times 10^{-31} \times v^2\)

\(v^2\) \(=\dfrac{4.806 \times 10^{-16}}{4.5545 \times 10^{-31}}\)  
\(v\) \(=\sqrt{1.055 \times 10^{15}}\)  
  \(=3.25 \times 10^7\ \text{ms}^{-1}\)  

 

The de Broglie wavelength of the electron is:

\(\lambda\) \(=\dfrac{h}{mv}\)  
  \(=\dfrac{6.626 \times 10^{-34}}{3.25 \times 10^7 \times 9.109 \times 10^{-31}}\)  
  \(=2.24 \times 10^{-11}\ \text{m}\)  

 
Frequency of the X-ray:

\(f=\dfrac{c}{\lambda}=\dfrac{3 \times 10^8}{2.24 \times 10^{-11}}=1.34 \times 10^{19}\ \text{Hz}\)

♦♦♦ Mean mark (b) 27%.
COMMENT: Multi-step solutions require clear and logical working.

PHYSICS, M8 2019 VCE 15 MC

Electrons pass through a fine metal grid, forming a diffraction pattern.

If the speed of the electrons was doubled using the same metal grid, what would be the effect on the fringe spacing?

  1. The fringe spacing would increase.
  2. The fringe spacing would decrease.
  3. The fringe spacing would not change.
  4. The fringe spacing cannot be determined from the information given.
Show Answers Only

\(B\)

Show Worked Solution

→ \(\lambda=\dfrac{h}{mv} \ \Rightarrow \  \lambda \propto \dfrac{1}{v}\)

→ If the velocity of the electron is doubled, the wavelength of the electron will halve.

→ Using Young’s double slit calculations:

\(\dfrac{d\Delta x}{D}=m \lambda\ \Rightarrow\  \Delta x \propto \lambda\)

→ Therefore, if lambda decreases so will the fringe spacing \((\Delta x)\).

\(\Rightarrow B\)

♦ Mean mark 40%.
COMMENT: Formulas from different syllabus areas required here.

PHYSICS, M8 2019 VCE 14* MC

Electrons are accelerated in an electron gun to a speed of 1.0 × 10\(^7\) m s\(^{-1}\).

The best estimate of the de Broglie wavelength of these electrons is

  1. 4.5 × 10\(^{-6}\) m
  2. 7.3 × 10\(^{-8}\) m
  3. 7.3 × 10\(^{-11}\) m
  4. 4.5 × 10\(^{-12}\) m
Show Answers Only

\(C\)

Show Worked Solution

\(\lambda=\dfrac{h}{mv}=\dfrac{6.626 \times 10^{-34}}{9.109 \times 10^{-31} \times 1 \times 10^7}=7.3 \times 10^{-11}\ \text{m}\)

\(\Rightarrow C\)

PHYSICS, M8 2020 VCE 16

A beam of electrons travelling at 1.72 × 10\(^5\) m s\(^{-1}\) illuminates a crystal, producing a diffraction pattern as shown in Figure 16. Ignore relativistic effects.
 

  1. Calculate the kinetic energy of one of the electrons. Show your working.  (2 marks)

  2. The electron beam is now replaced by an X-ray beam. The resulting diffraction pattern has the same spacing as that produced by the electron beam.

    Calculate the energy of one X-ray photon. Show your working.  (3 marks)

Show Answers Only

a.    \(0.084\ \text{eV}\)

b.    \(293\ \text{eV}\)

Show Worked Solution

a.     \(KE\) \(=\dfrac{1}{2}mv^2\)
    \(=\dfrac{1}{2} \times 9.109 \times 10^{-31} \times (1.72 \times 10^5)^2\)
    \(=1.3474\times 10^{-20}\ \text{J}\)
    \(=\dfrac{1.3474 \times 10^{-20}}{1.602 \times 10^{-19}}\)
    \(=0.084\ \text{eV}\)

 

b.     \(\lambda_e\) \(=\dfrac{h}{mv}\)
    \(=\dfrac{6.626 \times 10^{-34}}{9.109 \times 10^{-31} \times 1.72 \times 10^5}\)
    \(=4.23 \times 10^{-9}\ \text{m}\)
    \(=\lambda_{\text{x-ray}}\)

 

  \(E_{\text{x-ray}}\) \(=\dfrac{hc}{\lambda}\)
    \(=\dfrac{6.626 \times 10^{-34} \times 3 \times 10^8}{4.23 \times 10^{-9}}\)
    \(=4.7 \times 10^{-17}\ \text{J}\)
    \(=\dfrac{4.7 \times 10^{-17}}{1.602 \times 10^{-19}}\)
    \(=293\ \text{eV}\)
♦ Mean mark (b) 41%.

PHYSICS, M8 2020 VCE 18 MC

Quantised energy levels within atoms can best be explained by

  1. electrons behaving as individual particles with different energies.
  2. electrons behaving as waves, with each energy level representing a diffraction pattern.
  3. protons behaving as waves, with only standing waves at particular wavelengths allowed.
  4. electrons behaving as waves, with only standing waves at particular wavelengths allowed.
Show Answers Only

\(D\)

Show Worked Solution

→ This was explained by de Broglie’s work in determining electrons (all matter) can exhibit wave properties.

→ Quantised energy levels in the atom correspond to where electrons form standing waves due to there being an integer number of electron wavelengths.

\(\Rightarrow D\)

PHYSICS, M8 2021 VCE 17 MC

Which one of the following is closest to the de Broglie wavelength of a 663 kg motor car moving at 10 m s\(^{-1}\) ?

  1. \(10^{-37}\) m
  2. \(10^{-36}\) m
  3. \(10^{-35}\) m
  4. \(10^{-34}\) m
Show Answers Only

\(A\)

Show Worked Solution

\(\lambda=\dfrac{h}{mv}=\dfrac{6.626 \times 10^{-34}}{663 \times 10}=9.99 \times 10^{-38} \approx 10^{-37}\ \text{m}\)

\(\Rightarrow A\)

PHYSICS, M8 2022 VCE 17

A materials scientist is studying the diffraction of electrons through a thin metal foil. She uses electrons with an energy of 10.0 keV. The resulting diffraction pattern is shown in Figure 19.
 

  1. Calculate the de Broglie wavelength of the electrons in nanometres.  (4 marks)

  1. The materials scientist then increases the energy of the electrons by a small amount and hence their speed by a small amount.

    Explain what effect this would have on the de Broglie wavelength of the electrons. Justify your answer.  (3 marks)

Show Answers Only

a.    \(0.012\ \text{nm}\)

 

b.    Effects when speed of the electron increases by a small amount:

→ Momentum will increase by a small amount

→ As \(\lambda \propto \dfrac{1}{mv}\), if the momentum of the electron increases, its corresponding de Broglie wavelength will decrease.

Show Worked Solution

a.    Convert electron volts to joules:

\(\Rightarrow \ E=10 \times 10^3 \times 1.602 \times 10^{-19}=1.602 \times 10^{-15}\ \text{J}\)

\(E\) \(=\dfrac{1}{2}mv^2\)  
\(v\) \(=\sqrt{\dfrac{2E}{m}}\)  
  \(=\sqrt{\dfrac{2 \times 1.602 \times 10^{-15}}{9.109 \times 10^{-31}}}\)  
  \(=5.93 \times 10^7\)  

 

\(\therefore \lambda\) \(=\dfrac{h}{mv}\)  
  \(=\dfrac{6.626 \times 10^{-34}}{9.109 \times 10^{-27} \times 5.93 \times 10^7}\)  
  \(=1.23 \times 10^{-11}\ \text{m}\)  
  \(=0.012\ \text{nm}\)  

♦ Mean mark 42%.

b.    Effects when speed of the electron increases by a small amount:

→ Momentum will increase by a small amount

→ As \(\lambda \propto \dfrac{1}{mv}\), if the momentum of the electron increases, its corresponding de Broglie wavelength will decrease.

PHYSICS, M8 2022 VCE 14 MC

Which one of the following best provides evidence of electrons behaving as waves?

  1. photoelectric effect
  2. atomic emission spectra
  3. atomic absorption spectra
  4. diffraction of electrons through a crystal
Show Answers Only

\(D\)

Show Worked Solution

→ Diffraction is a wave phenomenon.

→ As electrons produce a diffraction pattern after passing through a crystal, they are behaving as waves.

\(\Rightarrow D\)

PHYSICS, M8 2023 VCE 17 MC

Which one of the following statements best explains why it is possible to compare X-ray and electron diffraction patterns?

  1. X-rays can exhibit particle-like properties.
  2. Electrons can exhibit wave-like properties.
  3. Electrons are a form of high-energy X-rays.
  4. Both electrons and X-rays can ionise matter.
Show Answers Only

\(B\)

Show Worked Solution

→ de Broglie developed an equation linking an objects momentum to its wavelength. 

→ At high speeds, the wavelength of electrons is similar to that of X-rays and so they can be compared.

\(\Rightarrow B\)

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:

\(F_c=F_B\ \ \Rightarrow \ \ \dfrac{mv^2}{r}=qvB \ \ \Rightarrow \ \ \dfrac{q}{m}=\dfrac{v}{Br}\)

♦♦ Mean mark 45%.

→ 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.

PHYSICS, M8 2023 HSC 7 MC

A proton and a neutron travel at the same speed.

Which statement correctly explains the difference between their de Broglie wavelengths?

  1. The proton has a longer wavelength because its mass is greater.
  2. The proton has a shorter wavelength because its mass is smaller.
  3. The neutron has a shorter wavelength because its mass is greater.
  4. The neutron has a longer wavelength because its mass is smaller.
Show Answers Only

\(C\)

Show Worked Solution

→ de Broglie wavelengths are given by the equation  \( \lambda = \dfrac{h}{mv}\)

→ \( \lambda \propto \dfrac{1}{m} \)

∴ Since the mass of a neutron is slightly greater than the mass of a proton, the neutron will have a shorter wavelength.

\(\Rightarrow C\)

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)

Show Answers Only

If scientific models are not consistent with observations and mathematical ideas, then they need to be changed. The historical progression of models of the atom is an example of this scientific method in action.

→ The Geiger-Marsden experiment involved shooting a beam of alpha particles at a thin sheet of gold foil. It was observed that most alpha particles passed through the gold however some bounced back.

→ Rutherford explained these observations in his model. He postulated that a small, dense positively charged nucleus caused the alpha particles to bounce back and that this nucleus was surrounded by orbiting electrons. The atom was mostly empty space so the majority of alpha particles passed through.

→ This model was limited however as an electron orbiting the nucleus would be accelerating and would radiate electromagnetic radiation, losing energy and spiralling into the nucleus.

→ Bohr overcame this limitation and improved the atomic model by analysing observations of the hydrogen spectrum. He postulated that electrons occupied specific energy orbits and could jump from one energy level to another and electrons travelling from a higher to lower energy orbit would emit a photon, corresponding to emission lines on hydrogen’s spectrum. 

→ 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))`.

→ This model was limited as it was only able to explain the hydrogen atom and wasn’t able to explain why electrons were quantised in such a way.

→ De Broglie built upon this model by postulating that electrons behaved as a wave. He stated that electrons behaved as standing waves with an integer number of wavelengths fitting the circumference of an orbit.

→ De Broglie’s contribution was critically supported by his mathematical model for calculating the associated wavelength `lambda=(h)/(mv)`

→ From these examples, it is clear that our understanding of the atom has been increased following observations and improved mathematical models.
 

Answers could also reference:

→ Thomson’s discovery of the electron.

→ Further contributions from Davisson-Germer as well as Schrodinger and Heisenberg.

Show Worked Solution

If scientific models are not consistent with observations and mathematical ideas, then they need to be changed. The historical progression of models of the atom is an example of this scientific method in action.

→ The Geiger-Marsden experiment involved shooting a beam of alpha particles at a thin sheet of gold foil. It was observed that most alpha particles passed through the gold however some bounced back.

→ Rutherford explained these observations in his model. He postulated that a small, dense positively charged nucleus caused the alpha particles to bounce back and that this nucleus was surrounded by orbiting electrons. The atom was mostly empty space so the majority of alpha particles passed through.

→ This model was limited however as an electron orbiting the nucleus would be accelerating and would radiate electromagnetic radiation, losing energy and spiralling into the nucleus.

→ Bohr overcame this limitation and improved the atomic model by analysing observations of the hydrogen spectrum. He postulated that electrons occupied specific energy orbits and could jump from one energy level to another and electrons travelling from a higher to lower energy orbit would emit a photon, corresponding to emission lines on hydrogen’s spectrum. 

→ 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))`.

→ This model was limited as it was only able to explain the hydrogen atom and wasn’t able to explain why electrons were quantised in such a way.

→ De Broglie built upon this model by postulating that electrons behaved as a wave. He stated that electrons behaved as standing waves with an integer number of wavelengths fitting the circumference of an orbit.

→ De Broglie’s contribution was critically supported by his mathematical model for calculating the associated wavelength `lambda=(h)/(mv)`

→ From these examples, it is clear that our understanding of the atom has been increased following observations and improved mathematical models.
 

Answers could also reference:

→ Thomson’s discovery of the electron.

→ Further contributions from Davisson-Germer as well as Schrodinger and Heisenberg.

PHYSICS, M8 2015 HSC 34d

In 1927, Davisson and Germer reported the results of an experiment in which they fired electrons at a crystal of nickel and observed how the electrons were scattered.

  1. State their conclusion, with reference to the results they obtained.   (2 marks)
  1. Explain the significance of this experiment to the Rutherford-Bohr model of the atom.   (3 marks)
Show Answers Only

i.    Experiment Results:

→ Davisson and Germer found that the electrons were not scattered in a random pattern, but formed an interference pattern after passage through the crystal.

→ This pattern is formed by constructive and destructive wave interference.

Conclusion:

→ Since interference is a phenomenon only observed with waves they concluded that electrons were also waves.
 

ii.   The Rutherford-Bohr model:

→ Postulated that electrons existed in fixed orbits. The model however, was unable to explain why only these orbits were stable.

→ The knowledge that electrons are waves provides a plausible explanation for this stability.

→ If electrons act as waves, as indicated by de Broglie, the electron can only exist in orbits where it experiences constructive interference.

Show Worked Solution

i.    Experiment Results:

→ Davisson and Germer found that the electrons were not scattered in a random pattern, but formed an interference pattern after passage through the crystal.

→ This pattern is formed by constructive and destructive wave interference.

Conclusion:

→ Since interference is a phenomenon only observed with waves they concluded that electrons were also waves.
 

ii.   The Rutherford-Bohr model:

→ Postulated that electrons existed in fixed orbits. The model however, was unable to explain why only these orbits were stable.

→ The knowledge that electrons are waves provides a plausible explanation for this stability.

→ If electrons act as waves, as indicated by de Broglie and experimentally shown by Davisson and Germer, the electron can only exist in orbits where it experiences constructive interference.


Mean mark (ii) 54%.

PHYSICS, M8 2017 HSC 34dii

How did de Broglie, and Davisson and Germer contribute to the modification of the Bohr model of the atom?   (3 marks)

Show Answers Only

→ Bohr’s model posed serious challenges for classical physicists who could not explain the stable electron orbits which were integral to this model.

→ de Broglie modified Bohr’s model by postulating that electrons exist as standing waves about an atom’s nucleus with each of Bohr’s stationary states (energy levels) being associated with various wavelengths.

→ An important feature of de Broglie’s model was that only integer multiples of the fundamental wavelength were possible.

→ This idea was then tested experimentally by Davisson and Germer, whose electron scattering experiments provided evidence that electrons were waves.

Show Worked Solution

→ Bohr’s model posed serious challenges for classical physicists who could not explain the stable electron orbits which were integral to this model.

→ de Broglie modified Bohr’s model by postulating that electrons exist as standing waves about an atom’s nucleus with each of Bohr’s stationary states (energy levels) being associated with various wavelengths.

→ An important feature of de Broglie’s model was that only integer multiples of the fundamental wavelength were possible.

→ This idea was then tested experimentally by Davisson and Germer, whose electron scattering experiments provided evidence that electrons were waves.


Mean mark 55%.

PHYSICS, M8 2019 HSC 21

Outline de Broglie's contribution to quantum mechanics. Support your answer with a relevant equation.   (2 marks)

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de Broglie proposed the dual wave-particle model of matter which postulated that particles, such as electrons possessed wave properties.

The equation to predict the wavelength of such particles is:

`lambda=(h)/(mv)`

Show Worked Solution

de Broglie proposed the dual wave-particle model of matter which postulated that particles, such as electrons possessed wave properties.

The equation to predict the wavelength of such particles is:

`lambda=(h)/(mv)`

PHYSICS, M7 2020 HSC 30b

  1. Calculate the wavelength of a proton travelling at 0.1\(c\).   (2 marks)
  1. Explain the relativistic effect on the wavelength of a proton travelling at 0.95\(c\).   (2 marks)
Show Answers Only

i.   `lambda=1xx10^(-14)` m

ii.  See Worked Solutions

Show Worked Solution
i.     `lambda` `=(h)/(mv)`
    `=(6.626 xx10^(-34))/(1.673 xx10^(-27)xx0.1 xx3xx10^(8))`
    `=1xx10^(-14)\ text{m}`

   

ii.    Due to momentum dilation:

→ The momentum of the proton is greater than that predicted by classical mechanics. 

→ Since  `lambda=(h)/(mv)\ \ =>\ \ lambda prop 1/(mv)`

→ The wavelength of the proton is shorter than would be predicted by classical mechanics.


♦ Mean mark (ii) 45%.

PHYSICS, M8 2021 HSC 29

Bohr, de Broglie and Schrödinger EACH proposed a model for the structure of the atom.

How does the nature of the electron proposed in each of the three models differ?   (5 marks)

Show Answers Only

Bohr’s model of the atom proposed that the electron was a negatively charged particle which orbits the nucleus in a circular path at discrete, quantised energy levels.

De Broglie’s model proposed that electrons had a dual wave/particle nature existing as stable standing waves around the nucleus.

Schrödinger’s quantum mechanical model described electrons as having a wave nature and existing as orbitals. His equation described a cloud surrounding the nucleus in which electrons had a high probability to be found.

Show Worked Solution

Bohr’s model of the atom proposed that the electron was a negatively charged particle which orbits the nucleus in a circular path at discrete, quantised energy levels.

De Broglie’s model proposed that electrons had a dual wave-particle nature existing as stable standing waves around the nucleus.

Schrödinger’s quantum mechanical model described electrons as having a wave nature and existing as orbitals. His equation described a cloud surrounding the nucleus in which electrons had a high probability to be found.


♦ Mean mark 49%.