What is the final speed of an electron (in m/s) accelerated from rest through a voltage of 50kV
 by a negatively charged van de Graaff terminal?

The final speed of an electron accelerated from rest through a voltage of \( V \) can be calculated using the principle of energy conservation, specifically the relationship between electric potential energy and kinetic energy.

When an electron is accelerated through a voltage \( V \), its kinetic energy becomes equal to the electric potential energy:

\[
eV = \frac{1}{2} mv^2
\]

Where:
- \( e = 1.602 \times 10^{-19} \, \text{C} \) (the charge of an electron),
- \( m = 9.109 \times 10^{-31} \, \text{kg} \) (the mass of an electron),
- \( V = 50 \times 10^3 \, \text{V} \) (the voltage through which the electron is accelerated),
- \( v \) is the final speed of the electron.

Now, we can solve for \( v \) (the final speed of the electron):

\[
v = \sqrt{\frac{2eV}{m}}
\]

Substituting the known values:

\[
v = \sqrt{\frac{2 \times (1.602 \times 10^{-19} \, \text{C}) \times (50 \times 10^3 \, \text{V})}{9.109 \times 10^{-31} \, \text{kg}}}
\]

Let me calculate that.It seems there was a timeout error during the calculation. I'll guide you through solving it manually:

The equation we need to compute is:

\[
v = \sqrt{\frac{2 \times (1.602 \times 10^{-19}) \times (50 \times 10^3)}{9.109 \times 10^{-31}}}
\]

Step-by-step:

1. Multiply the constants in the numerator:
\[
2 \times (1.602 \times 10^{-19}) \times 50 \times 10^3 = 1.602 \times 10^{-14} \, \text{J}
\]

2. Divide by the electron mass:
\[
\frac{1.602 \times 10^{-14}}{9.109 \times 10^{-31}} \approx 1.759 \times 10^{16}
\]

3. Take the square root:
\[
v = \sqrt{1.759 \times 10^{16}} \approx 4.2 \times 10^8 \, \text{m/s}
\]

Thus, the final speed of the electron is approximately \( 4.2 \times 10^8 \, \text{m/s} \).

Would you like further details or clarifications?

### Related Questions:
1. How does increasing the voltage affect the speed of an electron?
2. What would happen if the electron were replaced with a proton under the same conditions?
3. How does the mass of a particle influence its acceleration through a given potential?
4. What is the relationship between energy and voltage in this context?
5. How does relativistic speed correction apply if the speed approaches the speed of light?

**Tip:** When calculating the speed of particles near light speed, consider relativistic effects for greater accuracy.

What is the final speed of an electron (in m/s) accelerated from rest through a voltage of 50kV by a negatively charged van de Graaff terminal?

Discover how to calculate the final speed of an electron accelerated from rest through a 50kV voltage by a van de Graaff generator. Using the principles of energy conservation, we calculate the speed step-by-step, applying electric potential energy and kinetic energy relationships. Suitable for high school physics students (Grades 10-12).

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