1. What is the De Broglie Wavelength Formula?

The De Broglie wavelength formula relates the wavelength of a particle to its momentum. It demonstrates the wave-particle duality of matter, showing 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 (kg m/s)

Explanation: The equation shows that the wavelength of a particle is inversely proportional to its momentum - higher momentum results in shorter wavelength.

3. Importance of De Broglie Wavelength Calculation

Details: This calculation is fundamental in quantum mechanics for understanding particle behavior, electron microscopy, and various quantum phenomena where wave properties of matter are significant.

4. Using the Calculator

Tips: Enter the momentum value in kg m/s. The value must be positive and greater than zero for valid calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is wave-particle duality?
A: Wave-particle duality is the concept that every particle or quantum entity may be described as either a particle or a wave, exhibiting properties of both.

Q2: Who proposed this formula?
A: The formula was proposed by French physicist Louis de Broglie in 1924, for which he received the Nobel Prize in Physics in 1929.

Q3: What are typical wavelength values for common particles?
A: Electrons at typical energies have wavelengths around 10⁻¹⁰ m (similar to atomic spacing), while macroscopic objects have extremely small wavelengths that are not observable.

Q4: How is this used in electron microscopy?
A: Electron microscopes use the wave nature of electrons. Higher energy (momentum) electrons have shorter wavelengths, allowing for better resolution.

Q5: Does this apply to all particles?
A: Yes, the de Broglie wavelength applies to all matter, though the effects are only noticeable for very small particles like electrons, protons, and atoms.