1. What is the Electron Speed Calculator?

This calculator determines the speed of an electron based on its de Broglie wavelength, using fundamental constants of physics.

2. How Does the Calculator Work?

The calculator uses the de Broglie wavelength formula:

Where:

• \( v \) — Electron speed (m/s)
• \( h \) — Planck's constant (6.626 × 10⁻³⁴ J·s)
• \( m \) — Electron mass (9.11 × 10⁻³¹ kg)
• \( \lambda \) — Wavelength (m)

Explanation: The equation relates the wavelength of a particle to its momentum, with electrons behaving as both particles and waves.

3. Importance of Electron Speed Calculation

Details: Calculating electron speed from wavelength is fundamental in quantum mechanics, electron microscopy, and understanding atomic-scale phenomena.

4. Using the Calculator

Tips: Enter the wavelength in meters. The value must be positive and non-zero. Typical electron wavelengths are very small (nanometers or smaller).

5. Frequently Asked Questions (FAQ)

Q1: What is the de Broglie wavelength?
A: It's the wavelength associated with a moving particle, demonstrating wave-particle duality in quantum mechanics.

Q2: What are typical electron speeds?
A: Electron speeds vary widely but are often relativistic (significant fraction of light speed) in many applications.

Q3: Does this work for other particles?
A: Yes, but you'd need to substitute the appropriate mass for the particle in question.

Q4: What if my electron is relativistic?
A: This calculator uses non-relativistic approximation. For relativistic speeds, more complex equations are needed.

Q5: How precise are the constants used?
A: The constants are CODATA recommended values with very high precision (many significant digits).