What is the correct speed of alpha particles directed towards lead foil?

[hayowazzup]

Homework Statement

A beam of α particles with energy/particle = 2.86 MeV is directed towards lead foil.
What is the speed of the α particles?

Homework Equations

E = 1/2 mv^2
v = SQRT(2E/m)
v = SQRT((2)(2.86E+6)(1.602E-19) / (1.673E-27) ) = 23403526 m/s = 0.078c
but the ans is 0.039c which is half of the answer above. Why??

The Attempt at a Solution

 

[Hurkyl]

Did you do your calculations right? Did you use the right constants?

Punching

(2 * 2.86 MeV / (4 * (proton mass)))^(1/2) / c​

into google gives me the correct answer. (I've assumed the difference in proton and neutron masses are negligible)

Incidentally, I'm assuming you are neglecting relativistic effects?