Point A is at a potential of +250 V, and point B is at a potential of -150V. an alpha particle is a helium?

Question

oint A is at a potential of +250 V, and point B is at a potential of -150V. an alpha particle is a helium nuclues that contains two protons and two neutrons; the neutrons are electrically neutral. An alpha particle starts from rest at A and accelerates toward B. When the alpha particle arrives at B, what kinetic energy (in electron volts) does it have?

Answer 1

Now this is an interesting one. 1 ev = 1.602 x 10^-19 J and 1 proton charge is equal to 1.602 x 10 ^-19 C

Electric potential is basically potential energy per unit charge (1 volt = 1J/C), so at 250 V we have a potential energy for two protons of:

250 V * 2 * 1.062 x 10^-19 C = 8.01 x 10 ^-17 J * 1eV / 1.602 x 10^-19 J = 500 eV

For -150 V following the same math:

-150 V * 2 * 1.062 x 10^-19 C = -4.806 ^-17 J * 1eV / 1.602 x 10^-19 J = -300 eV

Since we have a change in potential energy we must have a corresponding change in kinetic energy to conserve energy.

change in KE + change in PE = 0

change in KE = - change in PE

change in KE = - (-300 - 500) eV

change in KE = 800 eV

Since we started at rest, the final KE is 800 eV.

Answer 2

work=charge on two protons xpotential difference
=(3.2x10^-19)(250-(-150))
=(3.2x10^-19)x400=1.28x10^-16 J=800 eV