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Electron Velocity Equation:
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The electron velocity equation \( v = \frac{h}{m \lambda} \) calculates the velocity of an electron based on its wavelength, using Planck's constant and the electron mass. This equation is derived from the de Broglie wavelength formula and is fundamental in quantum mechanics.
The calculator uses the electron velocity equation:
Where:
Explanation: This equation relates the wave-like properties of electrons to their particle-like properties, demonstrating the wave-particle duality principle in quantum mechanics.
Details: Calculating electron velocity from wavelength is crucial in various fields including quantum physics, electron microscopy, and semiconductor technology. It helps in understanding electron behavior at quantum levels and designing electronic devices.
Tips: Enter Planck's constant in J·s, electron mass in kg, and wavelength in meters. All values must be positive and non-zero. Use scientific notation for very small values (e.g., 6.626e-34).
Q1: What is the typical value of Planck's constant?
A: Planck's constant is approximately 6.626 × 10⁻³⁴ Joule seconds (J s).
Q2: What is the mass of an electron?
A: The electron mass is approximately 9.109 × 10⁻³¹ kilograms (kg).
Q3: Can this equation be used for other particles?
A: Yes, the de Broglie equation applies to all matter, but the mass value would need to be adjusted for different particles.
Q4: What are typical electron wavelengths?
A: Electron wavelengths are extremely small, typically on the order of 10⁻¹² meters for electrons in electron microscopes.
Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the input values, but actual electron behavior may be influenced by relativistic effects at very high velocities.