1. What is the De Broglie Wavelength?

The De Broglie wavelength is the wavelength associated with a moving particle, showing that matter has wave-like properties. It's a fundamental concept in quantum mechanics that demonstrates wave-particle duality.

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 (kg·m/s)

Explanation: The equation shows that the wavelength of a particle is inversely proportional to its momentum. Smaller, faster-moving particles have shorter wavelengths.

3. Importance of De Broglie Wavelength

Details: This concept is crucial for understanding quantum behavior, electron microscopy, and the wave nature of matter. It explains why quantum effects become significant at atomic scales.

4. Using the Calculator

Tips: Enter the particle's momentum in kg·m/s. The momentum must be greater than zero. For electrons, remember p = mv where m is mass and v is velocity.

5. Frequently Asked Questions (FAQ)

Q1: What particles exhibit De Broglie wavelength?
A: All matter has wave-like properties, but the effect is only noticeable for very small particles like electrons, protons, and atoms.

Q2: How small is the wavelength for macroscopic objects?
A: For everyday objects, the wavelength is extremely small (e.g., ~10⁻³⁴ m for a baseball) and thus unnoticeable.

Q3: What's the significance in quantum mechanics?
A: It explains quantization in atoms - electron orbits must be integer multiples of their wavelength.

Q4: Can this be observed experimentally?
A: Yes, through electron diffraction experiments and scanning tunneling microscopes.

Q5: How does temperature affect the wavelength?
A: Higher temperature means higher kinetic energy and momentum, resulting in shorter wavelengths.