# Neutron must travel so that kinetic energy = rest energy

Problem statement
How fast must a neutron be travelling relative to a detector in order to have a measured kinetic energy that is equal to its rest energy?

An "attempt"
I know
Ek = mc^2 - m0c^2

But if Ek = m0c^2, wouldn't the two terms cancel out from this equation? I am having trouble going about with it mathematically, and could use a few pointers if you guys don't mind helping out.

Where m0 is the rest mass.
m is the relativistic mass

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Pengwuino
Gold Member
No, why would they cancel? You would get

$$2m_0 c^2 = mc^2$$

where I assume you're using the concept of relativistic mass $$m = \gamma m_0$$.

Honestly, I have to say I overlooked that "-" sign. Thank you Pengwuino.