λ is proportional to?
Correct answer: C. 1/E for photons and 1/√ E for particles
- A. 1/E for both photons and particles
- B. 1/√ E for both photons and particles
- C. 1/E for photons and 1/√ E for particles
- D. 1/√ E for photons and 1/E for particles
Explanation
Option C is correct.The wavelength of a photon is inversely proportional to its energy, but for particles, the wavelength is inversely proportional to the square root of its energy. This is because the energy of a photon is given by the following equation: E = hν where: h is Planck's constant ν is the frequency of the photon The frequency of a photon is given by the following equation: ν = c/λ where: c is the speed of light λ is the wavelength of the photon Substituting the equation for ν into the equation for E, we get: E = h(c/λ) This means that E is inversely proportional to λ. For particles, the wavelength is given by the following equation: λ = h/p where: h is Planck's constant p is the momentum of the particle The momentum of a particle is given by the following equation: p = mv where: m is the mass of the particle v is the velocity of the particle Substituting the equation for p into the equation for λ, we get: λ = h/mv This means that λ is inversely proportional to the square root of E.
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Classical physics cannot explain blackbody radiation and related observations, leading to Planck’s quantum theory, in which energy is emitted or absorbed in discrete packets. Photons provide the particle model of light, with energy and momentum linked to frequency and wavelength, including the photoelectric effect and its threshold frequency.
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