What is the Wavelength of the Ejected Electron?

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SUMMARY

The discussion centers on calculating the wavelength of an ejected electron when a photon with a wavelength of 368 nm strikes a metal surface with a threshold frequency of 3.184 x 1014 Hz. The relevant equations include the relationship between frequency and wavelength, as well as the energy conservation equation: Eincident = Ethreshold + KE. To find the wavelength of the ejected electron, participants recommend using the kinetic energy formula KE = p2 / (2m) to determine momentum, followed by the de Broglie wavelength equation λ = h/p.

PREREQUISITES
  • Understanding of photon energy calculations
  • Familiarity with the photoelectric effect
  • Knowledge of de Broglie wavelength concepts
  • Basic principles of momentum in physics
NEXT STEPS
  • Study the photoelectric effect and its implications in quantum mechanics
  • Learn about de Broglie wavelength and its applications in particle physics
  • Explore the relationship between kinetic energy and momentum in quantum systems
  • Investigate the significance of threshold frequency in electron emission
USEFUL FOR

Students studying quantum mechanics, physics educators, and anyone interested in the principles of the photoelectric effect and electron behavior in metal surfaces.

mirandab17
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Homework Statement



The threshold frequency of a metal is 3.184 x 10^14 Hz. If a photon of wavelength 368 nm strikes the surface of the metal, what is the wavelength of the ejected electron?

Homework Equations


f (frequency) = c/(wavelength)
Eincident = Ethreshold + KE
E=fv(wavelength)

The Attempt at a Solution


Oh man... here it is. I bet I'm missing something huge but it's just been killing me.

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You're good up through the energy calculation. From there you can use:
$$KE = \frac{p^2}{2m}$$
to get a value for your momentum. Then just plug that number in to:
$$\lambda = \frac{h}{p}$$
and you get your answer.
 

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