An electron (mass m = 9.11e-31 kg) is accelerated in the uniform field E (E = 2.00e4 N/C) between two parallel charged plates. The separation of the plates is 1.10 cm. The electron is accelerated from rest near the negative plate and passes through a tiny hole in the positive plate.
What speed does it leave the hole (in m/s)? I have worked the problem with help from a prior question very similar, but cannot seem to produce a correct answer. May I see the work, not just the formula?
Let's see your work first. We'll tell you where you went wrong.
e*E*X is the kinetic energy acquired. Make usre X is in meters.
Set the KE equal to (1/2)mV^2 and solve for V.
To find the final speed of the electron as it leaves the hole, we can use the concept of electric potential energy and conservation of energy.
Let's break down the steps:
1. Determine the initial potential energy:
The initial potential energy of the electron can be calculated using the equation:
U = q * ΔV
where U is the potential energy, q is the charge of the electron, and ΔV is the potential difference between the plates.
Since the electron has a charge of -e (where e is the elementary charge), we have:
U = (-e) * ΔV
Given that the potential difference between the plates is ΔV = E * d (where E is the electric field strength and d is the separation between the plates), we can substitute the values:
U = (-e) * (E * d)
2. Determine the change in kinetic energy:
As the electron moves from rest near the negative plate to the tiny hole in the positive plate, the change in kinetic energy is equal to the negative of the initial potential energy, i.e., ΔK = -U.
Since the initial kinetic energy is 0 (electron starts from rest),
ΔK = K_final - K_initial = -U
3. Determine the final kinetic energy:
The final kinetic energy can be calculated using the equation:
K_final = 0.5 * m * v^2
where m is the mass of the electron and v is its final velocity.
Substituting the values:
0.5 * m * v^2 = -U
4. Solve for the final velocity:
We can rearrange the equation to solve for the final velocity (v):
v = sqrt(-2U/m)
Substituting the value of U, we get:
v = sqrt(2 * e * E * d / m)
Now, substitute the given values:
m = 9.11e-31 kg
E = 2.00e4 N/C
d = 1.10 cm = 1.10e-2 m
e = 1.60e-19 C
Plug in these values into the equation and calculate the result to get the final speed of the electron as it leaves the hole.
Please note that the final speed obtained is the magnitude of the velocity vector. The direction of the velocity can be determined by the electric field direction and the positive/negative charge of the electron.