1. What is the Electron Speed Formula?

The electron speed formula calculates the velocity of an electron accelerated through an electric potential difference. It's derived from the conservation of energy principle, equating the electron's kinetic energy to the work done by the electric field.

2. How Does the Calculator Work?

The calculator uses the electron speed formula:

Where:

• \( v \) — Electron speed (m/s)
• \( q \) — Electron charge (1.6 × 10^-19 C)
• \( V \) — Voltage (Volts)
• \( m \) — Electron mass (9.11 × 10^-31 kg)

Explanation: The formula shows that electron speed increases with the square root of the applied voltage, as the energy gained by the electron is proportional to the voltage.

3. Importance of Electron Speed Calculation

Details: Calculating electron speed is crucial in designing electron microscopes, cathode ray tubes, particle accelerators, and understanding fundamental physics experiments like the electron diffraction.

4. Using the Calculator

Tips: Enter the voltage in volts. The calculator will use the standard values for electron charge and mass. Voltage must be a positive number.

5. Frequently Asked Questions (FAQ)

Q1: Why does the formula use square root?
A: Because kinetic energy is proportional to velocity squared, so velocity is proportional to the square root of the energy.

Q2: What are typical electron speeds in experiments?
A: For 100V potential, electrons reach about 5.93×10⁶ m/s (about 2% of light speed).

Q3: Does this formula work for relativistic speeds?
A: No, for speeds approaching light speed (above ~10% of c), relativistic corrections are needed.

Q4: Why are the charge and mass constants?
A: These are fundamental physical constants for electrons. Different particles would have different values.

Q5: What affects the accuracy of this calculation?
A: The calculation assumes vacuum conditions and neglects thermal effects, quantum effects, and relativistic effects.