(adsbygoogle = window.adsbygoogle || []).push({}); "Free" electron...border between relativity and non-relativity

Hello guys...I have a couple of issues that I'm not exactly sure about...

1. The problem statement, all variables and given/known data

a) What does it mean to say that an electron is "free"?

b) To figure out the kinetic energy of a particle...one must first have to check if it's a non-relativistic case, or an ultra-relativistic case...my notes have it one should compute the value of [tex] T/mc^2[/tex] (T=kinetic energy)...but why do we have to do that?

2. Relevant equations

[tex] T/mc^2[/tex]

[tex]T=p^2/2m[/tex]

[tex] E=pc[/tex]

[tex]E=T=pc[/tex]

3. The attempt at a solution

a) I think "free" means the electron is moving under no potential? So...in that case...the total energy equals the kinetic energy?

b) I don't know why we have to compute the value of [tex] T/mc^2[/tex]...but I know if it's <<1 then it's a non-relativistic case, and we can use the formula [tex]T=p^2/2m[/tex] to find the Kinetic energy. If [tex] T/mc^2[/tex] is >>1 then it's a relativistic case, and we use [tex]E=T=pc[/tex] to solve for the kinetic energy? What is the definition of the border between non-relativistic and relatiticistic cases?

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# Free electron border between relativity and non-relativity

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