Proton-kinetic energy and speed question (please help me!)

Question

A proton has been accelerated from rest through a potential difference of -1000 V.

1. What is the proton's kinetic energy, in electron volts?
2. What is the proton's kinetic energy, in joules?
3. What is the proton's speed?

Answer 1

Picture two identical copper plates, each a square with 1 meter per side.

The plate on your left is connected to the positive terminal of a voltage source.

The plate on your right is connected to the negative terminal of that voltage source.

A tiny particle with Mass of 1.67262310E-27 Kilogram and Charge of +1.6021773349E-19 Coulomb (in other words, a proton) is at rest and loose on the surface of the positive 

plate.

With the Power switch open, the system is in the "Dead State"; when that switch is closed, the system is "Live" and energizes at almost the velocity of light.  

The positive plate takes on Electric Potential of 500 Volts.  

The negative plate goes to Electric Potential of -500 Volts.  

The tiny proton immediately loads with a tremendous potential energy and is violently shot across the distance between the plates by the powerful repulsion of the positive plate and irresistible attraction of the negative plate. It then smashes into the surface of the negative plate and immediately loses all potential (stored) energy and kinetic (active) energy.

The proton will then have traveled through a Potential Difference of (500 minus -500)

or 1000 Volts.

Equate loss in potential energy to gain in kinetic energy; this is shown by

q(V_positive − V_negative) = 0.5mv².

Then (1.6021773349E-19 Coulomb)(500 − -500) Joules Per Coulomb = 

0.5(1.67262310E-27 Kilogram)v² will yield the velocity of the proton as 

v = 437694.6562 meters per second.

Take Kinetic Energy In Joules as 0.5mv² or 0.5(1.67262310E-27 kg)(437694.6562 m/s)².

This last simplifies to 1.6021773349E-16 Joule. This is a tiny fraction of 1 Joule, which is the work done by a mass of 1 kilogram, accelerated by 1 meter per second every second, driving through a distance of 1 meter.

1.602177334E-16 Joule in Electron-Volts (or eV) is given by 

(1.602177334E-16 Joule) Divided By (1.6021773349E-19 Coulomb Per Electron)

equal to 1E3 [Electron-Dot-Joule-Per-Coulomb] or 1000 [e • J/C] or 1000 eV.

Answer 2

1) Energy of the proton will be

E=q.V=1(e).1000 V=1000 eV (The charge of a single photon is equal to charge of an electron which is called as elementary charge of 1 unit)

2) 1 eV= 1.6.10^-19 J so if we multiply the answer in Q1 with this number we will get the energy in Joules

E= 1000x 1.6x10^-19 = 1.6x10^-16 J.

3) We can calculate the speed by using the kinetic energy formula because the proton was accelerated under the potential difference.

K.E= 1/2 m.v²= 1.6x10^-16 J (Note that mass of the proton m= 1.67x10^-27 kg)

if we solve the equation for speed the answer will be V=4.37x10⁵ m/s