Is the soeed of an electron relativistic?

[number14]

Homework Statement

Determine the speed of an electron in a hydrogen atom (radius .5 * 10^-10 m) and state if it is relativistic. (Treat the electron as through it were in a circular orbit around the proton.) (Given that .1c and greater is relativistic)

Homework Equations

not sure...
L=L₀ (1-v^2/c^2)^1/2
a=v^2/r
?

The Attempt at a Solution

I don't really know where to start. I assume the fact that the electron has a centripetal acceleration and velocity comes into play somehow.

 

[number14]

solved it!

 

[nlightner]

Yes, the speed of an electron in a hydrogen atom is relativistic. The speed of an electron in a hydrogen atom can be calculated using the formula v=sqrt(ke^2/r) where k is the Coulomb constant, e is the charge of an electron, and r is the radius of the orbit. Plugging in the values given, we get v=2.19*10^6 m/s. This is much greater than 0.1c (the speed of light) and therefore, the speed of the electron is relativistic. This means that the electron's speed is a significant fraction of the speed of light and its motion must be described using the principles of relativity. The equations you have listed in the homework may also be used to calculate the relativistic effects on the electron's mass and energy.