What Is the Maximum Speed of an Alpha Particle with 2.34 MeV Kinetic Energy?

[Kommandant]

Homework Statement

An Alpha Particle is emitted with a kinetic energy of 2.34 MeV during a radioactive decay process. The maximum speed of the alpha particle is?

Homework Equations

KE=mv²
1 ev = 1.6x10^-19j

The Attempt at a Solution

$$\sqrt{(2.34x10^6)(1.6x10^-19)/4(1.6x10^-27)}$$

Unfortunately the manual uses this solution for the problem:

$$\sqrt{2(2.34x10^6)(1.6x10^-19)/4(1.6x10^-27)}$$

Could anyone explain to me where the 2 comes from?

 

[Kommandant]

Nevermind... I see what I did wrong..

KE= 1/2 mv^2 DUHHHH