At what velocity should relativity be taken into account

AI Thread Summary
Relativity should be considered when velocities approach a significant fraction of the speed of light (c), which is approximately 300,000,000 m/s. The discussed velocity of 6.5 x 10^6 m/s is about 2% of c, resulting in a minimal error of around 0.03% if relativistic effects are ignored. For most practical calculations, especially with limited precision, this velocity can be treated as non-relativistic. However, if higher precision is required or if velocities increase significantly, incorporating relativity becomes essential. Understanding the context and precision needed for calculations is crucial when determining the relevance of relativity.
moonkey
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Homework Statement


I have exams coming up and I'm just looking for an idea of when relativity should be taken into account. For example I'm just going over a question involving photoelectric effect and potential fields and de Broglie and all that jazz and the final velocity of the electron turns out to be around 6.5x106ms-1. Should I take relativity into account for this velocity or is it still safely within the margins of non-relativistic velocity? I'm thinking that it is safe to assume that it is non-relativistic but I would like some advice just in case such a question arises that involves a greater velocity.


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The Attempt at a Solution

I have exams coming up and I'm just looking for an idea of
 
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OOPS. Forget I said anything (it turned out to be not relevant, so I deleted my comment)
 
At a first glance, I'd say it depends on the precision that you want.
Since c is 300.000.000 m/s your speed is a 2% of c, which gives you an error of 0.03% if you ignore c (if I am not wrong).

If you use just only 3 figures (e.g. 0.134) in your data, then ignore it.
 
That makes perfectly good sense.

Thanks Quinzio
 

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