Alright, here's my question:

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And (very) partial answer:

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Honestly really wondering how I could actually fully answer this let alone set it out properly.

Hey!

I believe for part a), you could use the formula

. Where

is the charge of an electron

and

. This will enable you to find the speed

.

For part b), we can again use the same formula

to understand the situation. The idea before the formula is that kinetic energy is being converted to electric potential energy or vice versa. Therefore, in the context of this question since the proton is moving from a negative plate to a positive plate, the energy transformation we are interested in is conversion from kinetic energy to electric potential energy. Hence, qV tells us the amount of electric potential energy that is required for the proton to move and cross the positive plate. If the amount of kinetic energy energy that the proton possesses is less than qV, it won't be able to cross the plate but if it exceeds qV, it will be able to cross the plate.

But we know that the magnitude of the electrical charge of protons and electrons are the same so qV from part a) is still the same, and we know that the speed found in part a) is the speed of the proton initially. What we can see is that since the mass of the proton is greater than that of an electron,

for the proton will be greater than

so the proton will make it across the positive plate.

Hope this helps!