Wavelength of an electron homework

[Jules18]

Homework Statement

De Broglie postulated that the relationship λ=h/p is valid for relativistic particles. What is the de Broglie wavelength for a (relativistic) electron whose kinetic energy is 3.00 MeV?

-Electron has 3.00 MeV (or 4.8*10^-13 Joules)
-it's relativistic
-finding λ.

Homework Equations

h=6.63*10^-34

λ=h/p (obviously)

And I'm not sure if they're needed, but the relativistic eq's are:

KE = mc^2/sqrt(1-(v/c)^2)
p = mv/sqrt(1-(v/c)^2)

I'm not sure if this one applies to relativistic speeds:

E = hc/λ

The Attempt at a Solution

Attempt 1:

E = hc/λ

4.8E-13 = (6.63E-34)(3E8)/λ
λ = (6.63E-34)(3E8)/(4.8E-13)
λ = 4.14E-13 m

BUT answer key says 3.58E-13

If you could help, that would be great.
Sorry if it's too long, and I'm a little unfamiliar with relativistic eqn's so forgive me if I screwed up on them.

 

[diazona]

The equation you used, $E = hc/\lambda$, only applies to photons (or massless particles in general). So you're not going to need that one here. If you're familiar with the equation
$$E^2 = p^2c^2 + m^2c^4$$
I'd use that. If not, you can get the velocity from
$$E = \frac{mc^2}{\sqrt{1 - v^2/c^2}}$$
(note that that's total energy, not kinetic energy) and compute the momentum from that.

 

[Jules18]

Thanks very much for the help.