The electrical potential energy of a charge q located at a point at potential V is given by
Therefore, if the charge must move between two points at potential V1 and V2, the difference in potential energy of the charge will be
In our problem, the electron (charge e) must travel across a potential difference V. So the energy it will lose traveling from the metal to the detector will be equal to
Therefore, if we want the electron to reach the detector, the minimum energy the electron must have is exactly equal to the energy it loses moving from the metal to the detector:
Therefore, if the charge must move between two points at potential V1 and V2, the difference in potential energy of the charge will be
In our problem, the electron (charge e) must travel across a potential difference V. So the energy it will lose traveling from the metal to the detector will be equal to
Therefore, if we want the electron to reach the detector, the minimum energy the electron must have is exactly equal to the energy it loses moving from the metal to the detector: