Final answer:
To find the final speed of an electron accelerated through a given potential difference, use the conservation of energy to equate the electron's final kinetic energy to the change in electric potential energy, then solve for the velocity.
Step-by-step explanation:
To solve for the speed (v) of a free electron when equating the kinetic energy formula to the change in electric potential energy formula −qΔV, we apply the principle of conservation of energy.
The initial kinetic energy (KEi) is zero because the electron starts from rest, which leads to the final kinetic energy (KEf) being equal to the change in electric potential energy (PE). Thus, we can express this relationship as KEf = −qΔV. Using the kinetic energy formula, KE = (1/2)mv2, and substituting in for KEf, we get (1/2)mv2 = −qΔV. By rearranging the equation, we solve for v: v = √(−2qΔV/m).
Given a potential difference (ΔV) of 100 V and knowing the charge of an electron (q) as well as its mass (m), we can calculate the final speed of the electron by plugging in these values into the equation.