The change in electrical potential energy of the electron is given by:
[tex]\Delta U = e \Delta V[/tex]
where
e is the electron charge
[tex]\Delta V[/tex] is the potential difference between the initial and final point of the electron.
The electron moves by a distance d=4.5 m in the electric field of intensity [tex]E=325 N/C[/tex], so the potential difference between the initial and final location of the electron is
[tex]\Delta V= -E d= -(325 N/C)(4.5 m)=-1462.5 V[/tex]
where the negative sign is due to the fact that the electron is moving in the direction of the electric field, so it is moving from a point at higher potential to a point of lower potential, so the [tex]\Delta V[/tex] must be negative.
Therefore, the change in electrical potential energy of the electron is
[tex]\Delta U= e \Delta V=(-1.6 \cdot 10^{-19} C)(-1462.5 V)=2.34 \cdot 10^{-16} J[/tex]
