Final answer:
The potential energy of the charged particle when exposed to the voltage is calculated by multiplying the charge by the voltage, and the final velocity is determined by equating the kinetic energy to the work done by the potential energy and solving for velocity.
Step-by-step explanation:
To answer your question, we need to follow a two-step process to determine the potential energy and the final velocity of the particle with excess electrons when it is accelerated through a voltage.
(a) Potential Energy
The potential energy (PE) given to the particle by the electric field can be calculated using the formula:
PE = qV
where q is the charge of the particle and V is the voltage. Since we know the particle has 300 excess electrons, the charge q can be found by multiplying the elementary charge of an electron (e = 1.60 × 10−19 C) by the excess number of electrons. Then you multiply by the voltage (50 V) to find the potential energy.
(b) Final Velocity
The final velocity can be found using the work-energy principle, which states that the work done on the particle by the electric field will be equal to the kinetic energy (KE) of the particle when it leaves the electric field:
KE = ½ mv2
Since the work done (W) is equal to the potential energy gained (PE), you can set PE equal to KE and solve for the velocity v:
½ mv2 = qV
With the mass of the particle (0.040 g converted to kg) and the calculated charge q, you can rearrange the equation to solve for v and find the final velocity of the particle.