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Questions and Answers
What does the de Broglie relation express about matter?
What does the de Broglie relation express about matter?
Which equation represents the de Broglie relation?
Which equation represents the de Broglie relation?
What does the Uncertainty Principle state about position and momentum?
What does the Uncertainty Principle state about position and momentum?
In the equation Δx Δp ≥ ħ/2, what does Δp represent?
In the equation Δx Δp ≥ ħ/2, what does Δp represent?
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Which experiment confirmed the de Broglie relation through electron diffraction?
Which experiment confirmed the de Broglie relation through electron diffraction?
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What can be inferred about the wavelength of a particle as its momentum increases?
What can be inferred about the wavelength of a particle as its momentum increases?
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Which of the following experiments demonstrates the wave nature of electrons through an interference pattern?
Which of the following experiments demonstrates the wave nature of electrons through an interference pattern?
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Which principle is expressed as Δx Δp ≥ ħ/2?
Which principle is expressed as Δx Δp ≥ ħ/2?
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What aspect of the uncertainty principle does the gamma ray microscope experiment aim to verify?
What aspect of the uncertainty principle does the gamma ray microscope experiment aim to verify?
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How is the uncertainty in an electron's position defined during the diffraction of a beam of electrons?
How is the uncertainty in an electron's position defined during the diffraction of a beam of electrons?
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What consequence does the uncertainty principle have on the stability of atoms?
What consequence does the uncertainty principle have on the stability of atoms?
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Why can't electrons reside inside the nucleus, according to the uncertainty principle?
Why can't electrons reside inside the nucleus, according to the uncertainty principle?
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What role does the Compton effect play in the gamma ray microscope experiment?
What role does the Compton effect play in the gamma ray microscope experiment?
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What determines the atomic size based on the uncertainty principle?
What determines the atomic size based on the uncertainty principle?
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What is the effect of the uncertainty principle on measuring both position and momentum of an electron?
What is the effect of the uncertainty principle on measuring both position and momentum of an electron?
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In the context of the experiments discussed, the uncertainty principle is primarily associated with which of the following concepts?
In the context of the experiments discussed, the uncertainty principle is primarily associated with which of the following concepts?
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Study Notes
Wave-Particle Duality and Uncertainty Principle
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De Broglie Relation: λ = h/p, where λ is wavelength, h is Planck's constant, and p is momentum.
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Group Velocity: v = dw/dk = v = h/2πm
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Experiments on Matter Waves: Matter waves are microscopic phenomena, not macroscopic, and thus their wavelength is often small enough to not be perceptible in daily life.
- Example: A 10g bullet moving at 100 m/s has a wavelength of 6.6 x 10⁻³⁴ m.
- Electrons moving at 10⁶ m/s have a wavelength of 7.2 x 10⁻¹⁰ m, comparable to X-rays; thus, wave effects are observable.
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Davisson-Germer Experiment: Established the validity of the de Broglie relation by demonstrating electron diffraction by a nickel crystal.
- Electrons emitted from a heated filament, accelerated through a potential difference (50V), then diffracted by a nickel crystal.
- Observed maximum diffraction at a scattering angle of 50°.
- Calculated wavelength from diffraction pattern matched the de Broglie wavelength.
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Uncertainty Principle:
- Delta-x * Delta-p ≥ h/4π
- Ax and Ap represent the uncertainties in position and momentum, respectively
- A minimum uncertainty in position and momentum exists.
- The more precisely the position of a particle is known, the less precisely its momentum can be known, and vice versa.
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Gamma Ray Microscope: Imagine an electron being observed using a gamma ray microscope:
- The resolving limit of the microscope, Δx, relates to the wavelength, λ, of the gamma-rays used.
- Using gamma rays yields the smallest possible Δx (smallest possible uncertainty in position)
- The photons used scatter when interacting with the electron, introducing uncertainty in momentum as well (Δp)
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Electron in the Nucleus:
- If assumed electron resides in the nucleus, it's energy must be ≈ 9.89 MeV which is larger than the energy of emitted beta particles (2–3 MeV).
- Thus, electrons cannot reside inside the nucleus.
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Description
This quiz focuses on key concepts related to wave-particle duality and the uncertainty principle in quantum mechanics. It includes discussions on the De Broglie relation, group velocity, and experimental validations like the Davisson-Germer experiment. Test your understanding of these foundational principles of quantum physics.
