Final answer:
The speed of an electron being accelerated from rest by a uniform electric field in a vacuum can be found using the work-energy principle by equating the work done by the electric field to the kinetic energy of the electron. The required speed is found by solving the equation for kinetic energy, which includes the charge and mass of the electron, the strength of the electric field, and the distance between the plates.
Step-by-step explanation:
The question involves calculating the speed of an electron as it leaves a hole in a positive plate after being accelerated by a uniform electric field. Using the work-energy principle, we know that the work done by the electric field on the electron is equal to the change in the electron's kinetic energy. Since the electron starts from rest, all the work done on it will convert to kinetic energy.
The work done, W, can be calculated using the formula W = qEd, where q is the electron's charge, E is the magnitude of the electric field, and d is the separation between the plates. The electron's charge is -1.60 x 10-19 C, the electric field strength E is given as 1.45 x 104 N/C, and the separation d is 1.10 cm (which must be converted to meters, d = 0.011 m for the calculation).
The kinetic energy (KE) acquired by the electron is equal to the work done on it, KE = ½ mv2, where m is the mass of the electron and v is the velocity we need to find. We can set W = KE and solve for v, giving us v = √(2qEd/m). Plugging in the values, we get the final speed of the electron as it leaves the hole.