1. What Is The De Broglie Wavelength?

The De Broglie wavelength is a concept in quantum mechanics that proposes all matter exhibits wave-like properties. For electrons, this wavelength is calculated using the formula λ = h/p, where h is Planck's constant and p is the momentum of the electron.

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, with Planck's constant as the proportionality factor.

3. Importance Of Wavelength Calculation

Details: Calculating the De Broglie wavelength is essential for understanding quantum behavior of particles, electron diffraction experiments, and various applications in quantum mechanics and electron microscopy.

4. Using The Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of De Broglie wavelength?
A: It demonstrates the wave-particle duality of matter, showing that particles like electrons exhibit wave-like properties.

Q2: How is momentum related to wavelength?
A: Momentum and wavelength are inversely proportional - higher momentum results in shorter wavelength, and vice versa.

Q3: What are typical wavelength values for electrons?
A: Electron wavelengths are typically on the order of 10⁻¹⁰ to 10⁻¹² meters, depending on their energy and momentum.

Q4: Can this formula be applied to other particles?
A: Yes, the De Broglie formula applies to all matter, from electrons and protons to larger objects, though wave effects are negligible for macroscopic objects.

Q5: How is this used in electron microscopy?
A: The wavelength determines the resolution limit of electron microscopes - shorter wavelengths allow for higher resolution imaging.