1. What is the De Broglie Wavelength?

The De Broglie wavelength is the wavelength associated with a moving particle, demonstrating the wave-particle duality of matter. It shows that particles like electrons exhibit wave-like properties.

2. How Does the Calculator Work?

The calculator uses the De Broglie equation:

Where:

• \( \lambda \) — Wavelength (meters)
• \( h \) — Planck's constant (6.626 × 10⁻³⁴ J·s)
• \( p \) — Momentum of the particle (kg·m/s)

Explanation: The equation relates the wavelength of a particle to its momentum, showing that particles with higher momentum have shorter wavelengths.

3. Importance of Wavelength Calculation

Details: Calculating De Broglie wavelength is fundamental in quantum mechanics, important for understanding electron microscopy, quantum tunneling, and wave-particle duality experiments.

4. Using the Calculator

Tips: Enter the particle's momentum in kg·m/s. The value must be positive. For electrons, momentum can be calculated from voltage or kinetic energy.

5. Frequently Asked Questions (FAQ)

Q1: What particles exhibit De Broglie wavelength?
A: All matter exhibits wave-like properties, but it's most noticeable for very small particles like electrons, protons, and neutrons.

Q2: How does wavelength relate to particle size?
A: When the wavelength is comparable to the size of objects the particle interacts with, wave-like behavior becomes significant.

Q3: What's the wavelength of macroscopic objects?
A: Extremely small due to large momentum (e.g., a 1kg ball moving at 1m/s has λ ≈ 6.6×10⁻³⁴ m).

Q4: How is this used in electron microscopes?
A: Electrons accelerated to high energies have very short wavelengths, allowing higher resolution than light microscopes.

Q5: Can this be applied to photons?
A: Yes, but photons are massless particles where p = E/c, leading to the standard photon wavelength equation.