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

3. 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.

Actually, this "KE" expresson is giving the total energy, kinetic + rest mass energy, so

KE + mc^{2} = mc^{2}/sqrt(1-(v/c)^{2})

That's an approximation that applies at extremely relativistic speeds (say v>0.99c), and is strictly true only when v=c, i.e. for photons and other massless particles.

Since this is a moderately relativistic situation, E=hc/λ is not valid.

You could try using the KE + mc^{2} equation instead, but many problems like this one make use of this: