An electron is launched from the negative plate. It strikes the positive plate at a speed of 2.3×10^7 m/s. What was the electron's speed as it left the negative plate?

the voltage is 650V
and the charge of q1 is 1.7*10^-9 and the charge of q2 is -1.7*10^-9

The kinetic energy gained going from the negative plate to the postivie plate is

E = e*V,
where e is the electron charge.

(1/2)*m*(V2^2 - V1^2) = E

Solve for the final velocity, V2
V1 = 2.3*10^7 m/s

m is the electron mass and e is its charge.

You don't need to know the charges on the two plates.

Well, this electron seems to have quite the electrifying journey! To determine its initial speed, we need to consider the potential difference (voltage) and the charge. However, since the charges cancel each other out, let's move on to the voltage.

Given that the voltage is 650V, it implies that the electron gained energy as it moved from the negative plate to the positive plate. To find the electron's initial speed, we can use the equation:

ΔE = q * V

Where ΔE is the change in kinetic energy, q is the charge, and V is the voltage. Since ΔE = mv²/2, we can solve for v (the initial speed):

mv²/2 = q * V

Let's plug in the values. The mass of an electron is approximately 9.10938356 × 10^-31 kg (don't you just love these precise numbers?):

(9.10938356 × 10^-31 kg) * v² / 2 = (1.7 × 10^-9 C) * (650 V)

Now, let's see if we can solve this equation and find the electron's initial speed!

To determine the speed of the electron as it left the negative plate, we can use the conservation of energy and the equation for electric potential energy.

The electric potential energy (PE) gained by the electron is equal to the work done by the electric field. It can be calculated using the equation:

PE = q1 * V

Where:
- PE is the electric potential energy
- q1 is the charge of the electron
- V is the voltage

Given that the voltage (V) is 650V and the charge of the electron (q1) is 1.7*10^-9 C, we can calculate the electric potential energy (PE) gained by the electron:

PE = (1.7*10^-9 C) * (650V)
PE = 1.105 × 10^-6 J

Next, we can use the conservation of energy to equate the potential energy gained by the electron to its kinetic energy at the positive plate. The kinetic energy (KE) of the electron can be calculated using the equation:

KE = (1/2) * m * v^2

Where:
- KE is the kinetic energy
- m is the mass of the electron
- v is the speed of the electron

We know the speed of the electron when it strikes the positive plate, which is 2.3×10^7 m/s. However, we need to find the mass of the electron to calculate its initial speed. The mass of an electron is approximately 9.10938356 × 10^-31 kg.

By equating the potential energy (PE) and kinetic energy (KE):

PE = KE
1.105 × 10^-6 J = (1/2) * (9.10938356 × 10^-31 kg) * v^2

Rearranging the equation to solve for v:

v^2 = (2 * 1.105 × 10^-6 J) / (9.10938356 × 10^-31 kg)
v^2 = 2.42175 × 10^24 m^2/s^2

Taking the square root of both sides:

v = √(2.42175 × 10^24 m^2/s^2)
v ≈ 1.555 × 10^12 m/s

Therefore, the speed of the electron as it left the negative plate was approximately 1.555 × 10^12 m/s.

To find the electron's speed as it left the negative plate, we can use the principle of energy conservation. Here's how to approach the problem:

1. Begin by determining the electric potential energy change (ΔPE) between the electron at the negative plate and the electron at the positive plate.

2. The electric potential energy change can be calculated using the formula: ΔPE = q1 * ΔV, where q1 is the charge of the electron (1.6 x 10^-19 C) and ΔV is the change in voltage.

3. In this case, the change in voltage is given as 650V. So, ΔPE = (1.6 x 10^-19 C) * (650V).

4. Now, since energy is conserved, the change in potential energy must be equal to the change in kinetic energy (ΔKE) of the electron.

5. The kinetic energy change can be calculated using the formula: ΔKE = (1/2) * m * (v_final^2 - v_initial^2), where m is the mass of the electron (9.11 x 10^-31 kg), v_final is the final velocity (2.3 x 10^7 m/s), and v_initial is the initial velocity that we need to find.

6. Rearrange the equation to solve for v_initial: v_initial = sqrt((2 * ΔKE / m) + v_final^2).

7. Use the known values to calculate ΔKE: ΔKE = q1 * ΔV.

8. Calculate v_initial using the obtained values and the formula from step 6.

By following these steps, you can find the speed of the electron as it left the negative plate.