De Broglie wavelength, kinetic energy

[ajmCane22]

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!

 

[gneill]

Check the velocity that you calculate. How does it compare to c?

 

[ajmCane22]

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?

 

[gneill]

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.