An electron moves from one plate to another across which there is a potential difference of 2000 V.

a) Find the speed with which the electron
strikes the positive plate.

For this problem, I used the Potential difference equation: (2000)(1.60x10^-19)=3.2E-16=delta PE
I was going to use the equation PEi+KEi=KEf+PEf to find the speed of the electron. Is that right?

Yes, that is correct, but remember that the initial Kinetic Energy (KEi) is zero in this case.

Once you know KEf, you can calculate V

Yes, you are correct in using the conservation of energy equation to find the speed of the electron. Here's a step-by-step explanation on how to solve the problem:

Step 1: Calculate the potential energy difference (ΔPE) using the formula ΔPE = q * ΔV, where q is the charge of the electron (1.60x10^-19 C) and ΔV is the potential difference (2000 V). So, ΔPE = (1.60x10^-19 C) * (2000 V) = 3.20x10^-16 J.

Step 2: Apply the conservation of energy equation, which states that the initial total energy (potential energy + kinetic energy) is equal to the final total energy. Mathematically, it can be written as: PEi + KEi = KEf + PEf.

Step 3: Since the electron starts from rest at the negative plate, the initial kinetic energy (KEi) is zero. So, the equation becomes: PEi = KEf + PEf.

Step 4: Substitute the known values into the equation. The initial potential energy (PEi) is the calculated ΔPE (3.20x10^-16 J). The final potential energy (PEf) is zero since the electron has already reached the positive plate. Therefore, the equation becomes: 3.20x10^-16 J = KEf + 0.

Step 5: Solve for the final kinetic energy (KEf) of the electron by isolating it in the equation. KEf = 3.20x10^-16 J.

Step 6: The final kinetic energy (KEf) can also be expressed as KEf = (1/2)mv^2, where m is the mass of the electron (9.11x10^-31 kg) and v is the speed we want to find. Substitute the values: (1/2)(9.11x10^-31 kg)(v^2) = 3.20x10^-16 J.

Step 7: Solve for v by isolating it in the equation. Divide both sides by (1/2)(9.11x10^-31 kg): v^2 = (3.20x10^-16 J) / [(1/2)(9.11x10^-31 kg)].

Step 8: Take the square root of both sides to find v: v = √[(3.20x10^-16 J) / [(1/2)(9.11x10^-31 kg)]].