Wave-particle duality
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Describe the evidence that the photoelectric effect provides for the particulate nature of electromagnetic radiation.
The photoelectric effect demonstrates that light energy is delivered in discrete packets called photons. Electrons are emitted instantaneously only when the photon energy exceeds the work function, suggesting a particle-like interaction rather than a continuous wave absorption.
Explain how electron diffraction provides evidence for the wave nature of particles.
Electron diffraction, similar to X-ray diffraction, produces interference patterns when electrons pass through a crystal lattice. This demonstrates that electrons, traditionally considered particles, exhibit wave-like behavior by undergoing diffraction and interference.
Define the de Broglie wavelength.
The de Broglie wavelength (λ) is the wavelength associated with a moving particle, relating its momentum to its wave-like properties. It shows that particles, such as electrons, also have a characteristic wavelength.
State the formula for the de Broglie wavelength and define each term.
λ = h / p, where λ is the de Broglie wavelength, h is Planck's constant (6.63 x 10⁻³⁴ Js), and p is the momentum of the particle (p = mv, where m is mass and v is velocity).
Calculate the de Broglie wavelength of an electron with a momentum of 1.0 x 10⁻²⁴ kg m/s.
Using λ = h / p, where h = 6.63 x 10⁻³⁴ Js and p = 1.0 x 10⁻²⁴ kg m/s, then λ = (6.63 x 10⁻³⁴) / (1.0 x 10⁻²⁴) = 6.63 x 10⁻¹⁰ m or 0.663 nm.
Explain why macroscopic objects do not display noticeable wave-like behavior.
Due to their large mass, macroscopic objects have very small de Broglie wavelengths (λ = h/mv). These wavelengths are so small that diffraction and interference effects are negligible and undetectable in everyday observations.
Describe how increasing the momentum of a particle affects its de Broglie wavelength.
Increasing the momentum of a particle decreases its de Broglie wavelength. Since λ = h/p, wavelength is inversely proportional to momentum. A higher momentum results in a shorter wavelength.
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