De Broglie wavelength, kinetic energy

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Homework Help Overview

The problem involves calculating the kinetic energy of an electron based on its de Broglie wavelength, with specific wavelengths corresponding to atomic and nuclear sizes. The original poster has successfully calculated the kinetic energy for one case but is struggling with the second, indicating a significant discrepancy in their result.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to calculate kinetic energy using a specific formula but questions their result for the second part of the problem. Some participants suggest checking the velocity calculated from the kinetic energy, while others raise concerns about the implications of relativistic effects at high energies.

Discussion Status

The discussion is ongoing, with participants exploring the implications of the calculations and questioning the assumptions made regarding velocity and relativistic effects. Guidance has been offered regarding the need to consider relativistic formulas if the calculated velocities approach significant fractions of the speed of light.

Contextual Notes

The original poster has indicated that they are converting kinetic energy from Joules to electronvolts, and there is a concern about the validity of their calculations in light of relativistic considerations.

ajmCane22
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Homework Statement



(a) Find the kinetic energy of an electron whose de Broglie wavelength is equal to 0.63 Å, a typical atomic size.

Ke = 379 eV

(b) Repeat part (a) for an electron with a wavelength equal to 1.7 x 10-15 m, a typical nuclear size.

Ke = _____eV


Homework Equations



Ke = h2 / λ2(2m)

The Attempt at a Solution



I got part (a), but for part be I calculated Ke = 5.217e11 which is "significantly different" from the correct answer. I tried getting help from Cramster and they provided me with the same answer. What am I doing wrong? Please help!
 
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Check the velocity that you calculate. How does it compare to c?
 
I don't understand. I'm not calculating velocity? I'm calculating kinetic energy in Joules and converting it to eV. Where do c and v come in?
 
ajmCane22 said:
I don't understand. I'm not calculating velocity? I'm calculating kinetic energy in Joules and converting it to eV. Where do c and v come in?

When the energies get high enough the velocities will approach the speed of light. Then you need to take Relativistic effects into account. Check the velocity implied by the KE using Newtonian methods. If it's more than about 2/3 of c (or *gasp* greater than c!) you should be using the Relativistic formulas instead.
 

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