# Mv^2 or 1/2mv^2

combining wavelength(&)=h/mv and e=hv/& , we get e=mv^2
but kinetic energy is 1/2mv^2. where is other half?

Hootenanny
Staff Emeritus
Gold Member
combining wavelength(&)=h/mv and e=hv/& , we get e=mv^2
but kinetic energy is 1/2mv^2. where is other half?
Kinetic energy only takes the form 1/2mv2 in classical mechanics, which is only valid for low velocities. The full expression for relativistic kinetic energy is

$$T = mc^2\left(\gamma-1\right)$$

You should also note that your first two expression are only valid for v = c.

Fredrik
Staff Emeritus