How Fast Do Photoelectrons Travel in Potassium Under 250 nm Light?

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SUMMARY

The maximum speed of photoelectrons in potassium illuminated by 250 nm light is calculated using the energy of the photons and the work function of potassium. The initial calculation yielded an incorrect speed of 2.42x1015 m/s, exceeding the speed of light. Correcting the kinetic energy by converting electron volts to joules resulted in a more reasonable speed of 9.7x105 m/s. This demonstrates the importance of unit consistency in physics calculations.

PREREQUISITES
  • Understanding of photoelectric effect principles
  • Familiarity with energy conversion between electron volts and joules
  • Knowledge of basic kinematics and equations of motion
  • Proficiency in dimensional analysis for verifying calculations
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  • Study the photoelectric effect in detail, focusing on the work function of various materials
  • Learn about energy conversion techniques, specifically between electron volts and joules
  • Explore advanced kinematics, including relativistic effects on particle speeds
  • Review dimensional analysis methods to ensure unit consistency in physics problems
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Physics students, researchers in material science, and anyone interested in the dynamics of photoelectrons and the photoelectric effect.

Calmeir
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Alright, I am having some trouble with the following problem, because my solution I arrive at seems to be way too large. The problem is:

What is the maximum photelectron speed if potassium is illuminated with light of 250 nm?

From that I have

λ = 250 nm
f = c/λ = 3x10^8 / 250x10^-9 = 1.2x10^15
Eo of potassium = 2.3 eV

From there I tried getting the velocity by obtaining the kinetic energy.

Eelec = hf = (4.14x10^-15)(1.2x10^15) = 4.968
Kmax = Eelec - Eo = 4.968 - 2.3 = 2.668

V = √2K/m = √2(2.668)/(9.11x10^-31) = 2.42x10^15 m/s

So my calculated answer is 2.42x10^15 m/s which is much faster than the speed of light, so I know it must be wrong. I can't seem to figure out another way to arrive at an answer though. Any help is much appreciated.
 
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Your units don't match. You either need to convert the electrons energy to joules or it's mass to eV/c^2 (that's about 511keV/c^2).
Doing a bit of dimensional analysis is usually useful if you get bizarre results from a calculation.
 
Ok, so taking the K of 2.668 eV and converting to joules I got 4.3x10^-19, then plugging those results into the my final equation I ended up with 9.7x10^5 m/s which sounds much more reasonable, but I just want to double check that I did that portion correctly. Was that the result you ended up with?
 

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