Final answer:
The proton's speed after 44.4 ns is approximately 216.8 m/s, while the electron's speed is approximately -3.98 x 10^12 m/s.
Step-by-step explanation:
In a uniform electric field, particles experience a constant force that accelerates them. The force experienced by a charged particle in an electric field is given by the equation F = qE, where F is the force, q is the charge of the particle, and E is the electric field strength. Since the electron and proton have opposite charges, the direction of their forces will be opposite.
- First, let's calculate the force on the proton. Given that the electric field strength is 506 N/C, and the charge of a proton is 1.6 x 10^-19 C, we can calculate the force as:
F = qE = (1.6 x 10^-19 C)(506 N/C) = 8.16 x 10^-17 N
- The acceleration of the proton can be calculated using the equation F = ma, where F is the force, m is the mass of the object, and a is the acceleration. The mass of a proton is approximately 1.67 x 10^-27 kg.
F = ma = (1.67 x 10^-27 kg)(a)
a = F / m = (8.16 x 10^-17 N) / (1.67 x 10^-27 kg) ≈ 4.89 x 10^9 m/s^2
- Similarly, we can calculate the force on the electron:
F = qE = (-1.6 x 10^-19 C)(506 N/C) = -8.16 x 10^-17 N
- And the acceleration of the electron:
a = F / m = (-8.16 x 10^-17 N) / (9.11 x 10^-31 kg) ≈ -8.96 x 10^13 m/s^2
- The speeds of the particles after 44.4 ns can be calculated using the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.
Since the particles are initially at rest, their initial velocities (u) are 0 m/s. Therefore, the final velocities (v) can be calculated as:
- Final velocity of the proton:
v = u + at = 0 + (4.89 x 10^9 m/s^2)(44.4 x 10^-9 s) ≈ 216.8 m/s
- Final velocity of the electron:
v = u + at = 0 + (-8.96 x 10^13 m/s^2)(44.4 x 10^-9 s) ≈ -3.98 x 10^12 m/s