(1) how much work is required to stop an electron
(m = 9.11 x 10-31 kg) which is moving with a speed
of 1.90 x 10 m/s?

Explanation:

We can solve the problem by using the work-energy theorem: in fact, the work done on the electron must be equal to its change in kinetic energy, therefore

where

is the mass of the electron

v = 0 is the final velocity of the electron (it comes to a stop)

u is the initial velocity of the electron

In the problem, we are told that the electron is initially moving at

Therefore, the work required to stop is is

and the work is negative since it is in the opposite direction to the motion of the electron.