We can figure out its gamma factor from

Plugging in **m = 9.1 x 10^ ^{-31} kg,** we find

The velocity of this electron is going to be VERY close
to the speed of light. We might encounter round-off
problems if we just plug these values into a calculator.
Therefore, I'm going to use the BINOMIAL EXPANSION
to derive an expression for the velocity of the electron
which will not suffer from roundoff.
My expression will be in terms of **c**,
not in meters per second.

To find the the time it takes electron A to reach the Earth, I will use the BINOMIAL EXPANSION a second time:

Now, let's look at the other electron, which has twice as much energy.

We can figure out its gamma factor from

We can then derive the velocity of electron B

The time it takes for electron B to reach the Earth is

Therefore, the high-energy electron B reaches the Earth slightly earlier than the low-energy electron A, by a difference of