The speed of an electron is 0.9999c. In a 3 km accelertor what isthe length in t

Question

The speed of an electron is 0.9999c. In a 3 km accelertor what isthe length in the electron's reference frame? The answer on here is 0.212 m gotten from L'=L    L'=L/ 1-(v/c)ˆ2 where L' is the length in the electron's frame.
But when I calculate 3000/1-0.9999ˆ2 the answer is not 0.212 m but 212137 m.
What's the deal?? The answer on here is 0.212 m gotten from L'=L    L'=L/ 1-(v/c)ˆ2 where L' is the length in the electron's frame.
But when I calculate 3000/1-0.9999ˆ2 the answer is not 0.212 m but 212137 m.
What's the deal??

Explanation / Answer

3 km is the length measured in the lab and is the proper length in the electron's reference frame, the length is contracted andequal to 3000(1 - 0.99992) = 0.212 m

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