1. What is the De Broglie Wavelength Formula?

The De Broglie wavelength formula, proposed by Louis de Broglie in 1924, describes the wave-like behavior of particles. It states that every moving particle has an associated wavelength, connecting particle properties with wave properties in quantum mechanics.

2. How Does the Calculator Work?

The calculator uses the De Broglie wavelength formula:

Where:

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

Explanation: The formula shows that the wavelength of a particle is inversely proportional to its momentum. Higher momentum particles have shorter wavelengths.

3. Importance of De Broglie Wavelength

Details: The De Broglie hypothesis was fundamental to the development of quantum mechanics. It explains wave-particle duality and has applications in electron microscopy, quantum computing, and understanding atomic structure.

4. Using the Calculator

Tips: Enter the momentum value in kg m/s. The momentum must be greater than zero. The calculator will compute the corresponding de Broglie wavelength using Planck's constant.

5. Frequently Asked Questions (FAQ)

Q1: What is wave-particle duality?
A: Wave-particle duality is the concept that every particle exhibits both wave-like and particle-like properties. The De Broglie wavelength quantifies the wave aspect of particles.

Q2: How is momentum related to wavelength?
A: Momentum and wavelength are inversely proportional. As momentum increases, the de Broglie wavelength decreases, and vice versa.

Q3: What are typical de Broglie wavelengths?
A: Macroscopic objects have extremely small wavelengths (undetectable), while subatomic particles like electrons have wavelengths comparable to atomic sizes.

Q4: Can this formula be used for photons?
A: Yes, for photons, p = E/c, and the formula gives the same result as λ = c/ν, demonstrating consistency between particle and wave descriptions.

Q5: What are practical applications?
A: Electron microscopes use the wave nature of electrons, and the formula is crucial in quantum mechanics calculations, semiconductor physics, and material science.