Law of conservation of energy:

$\overline{){{\mathbf{K}}}_{{\mathbf{i}}}{\mathbf{+}}{{\mathbf{U}}}_{{\mathbf{i}}}{\mathbf{+}}{{\mathbf{W}}}_{{\mathbf{nc}}}{\mathbf{=}}{{\mathbf{K}}}_{{\mathbf{f}}}{\mathbf{+}}{{\mathbf{U}}}_{{\mathbf{f}}}}$, where W_{nc} is the work done by non-conservative forces such as friction.

In this case, we do not have W_{nc} since there are no non-conservative forces.

W_{nc} = 0

Since the electron is in motion, the initial potential energy is zero.

U_{i} = 0

Also, K_{f} = 0 since the electron is coming to rest.

Kinetic energy is expressed as:

$\overline{){\mathbf{K}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{{\mathbf{mv}}}^{{\mathbf{2}}}}$

What potential difference is needed to stop an electron that has an initial velocity V = 6.0 × 10^{5} m/s?

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