Question

The electron and proton accelerated from rest in opposite directions through a 1.40 MV potential difference.

-calculate the final speed of proton (not relative) and then calculate the speed of the electron (relative) and then calculate relative to P

Answer 1

kinetic energy = qV

0.5mv^2 = qV

for proton

0.5*1.67*10^-27*v^2 = 1.6*10^-19*1.4*10^6

v = 1.64*10^7 m/s

for an electron

0.5*9.11*10^-31*v^2 = 1.6*10^-19*1.4*10^6

v = 7.01*10^8 m/s

speed of electron relative to P = (7.01*10^8 - 1.64*10^7) = 6.85*10^7 m/s

Answer 2

To solve this problem, we can use the principles of energy conservation and the fact that the potential difference is equal to the change in electric potential energy per unit charge.

1. Calculate the final speed of the proton: Given: Potential difference (V) = 1.40 MV = 1.40 * 10^6 V Charge of the proton (q) = +1.6 * 10^-19 C (Coulombs) Mass of the proton (m) = 1.67 * 10^-27 kg

The change in electric potential energy of the proton is given by: ΔPE = q * V

The change in kinetic energy of the proton is equal to the change in potential energy: ΔKE = ΔPE

Since the proton starts from rest, the initial kinetic energy is zero: Initial KE = 0

The final kinetic energy of the proton is given by: Final KE = 0.5 * m * v^2

Therefore, we can equate the change in kinetic energy to the change in potential energy: ΔKE = Final KE - Initial KE = 0.5 * m * v^2 - 0 = q * V

Solving for the final speed of the proton (v): 0.5 * m * v^2 = q * V v^2 = (2 * q * V) / m v = sqrt((2 * q * V) / m)

Substituting the known values: v = sqrt((2 * (1.6 * 10^-19 C) * (1.40 * 10^6 V)) / (1.67 * 10^-27 kg))

Calculate the value to find the final speed of the proton.

2. Calculate the speed of the electron (relative to the proton): The electron has the same magnitude of charge as the proton but opposite sign, so its charge is -1.6 * 10^-19 C.

Using the same principle of energy conservation, we can calculate the speed of the electron relative to the proton. The potential difference is the same for both particles, but the signs of their charges are different.

The final kinetic energy of the electron relative to the proton is given by: Final KE (relative) = 0.5 * m * v(electron-relative)^2

Since the electron starts from rest relative to the proton, the initial kinetic energy is zero: Initial KE (relative) = 0

Therefore, we can equate the change in kinetic energy to the change in potential energy: ΔKE (relative) = Final KE (relative) - Initial KE (relative) = 0.5 * m * v(electron-relative)^2 - 0 = q * V

Solving for the speed of the electron relative to the proton (v(electron-relative)): 0.5 * m * v(electron-relative)^2 = q * V v(electron-relative)^2 = (2 * q * V) / m v(electron-relative) = sqrt((2 * q * V) / m)

Substituting the known values: v(electron-relative) = sqrt((2 * (1.6 * 10^-19 C) * (1.40 * 10^6 V)) / (9.11 * 10^-31 kg))

Calculate the value to find the speed of the electron relative to the proton.

3. Calculate the speed of the electron relative to the lab frame (relative to P): To find the speed of the electron relative to the lab frame, we need to consider the velocities of both the proton and the electron relative to the lab frame.

Since the proton's final speed is known, we can subtract it from the speed of the