1. What is De Broglie's Theory?

De Broglie's hypothesis states that all matter exhibits wave-like properties. The wavelength (λ) of a particle is related to its momentum (p) through Planck's constant (h), while the frequency (f) is related to its energy (E).

2. How Does the Calculator Work?

The calculator uses De Broglie's equations:

Where:

• \( \lambda \) — Wavelength (meters)
• \( f \) — Frequency (Hertz)
• \( h \) — Planck's constant (6.626 × 10⁻³⁴ J s)
• \( p \) — Momentum (kg m/s)
• \( E \) — Energy (Joules)

Explanation: These equations demonstrate the wave-particle duality of matter, showing that particles like electrons have both particle and wave characteristics.

3. Importance of Wavelength and Frequency Calculation

Details: Calculating the de Broglie wavelength and frequency is crucial for understanding quantum mechanical behavior, electron microscopy, and various applications in modern physics and nanotechnology.

4. Using the Calculator

Tips: Enter momentum in kg m/s and energy in Joules. Both values must be positive numbers. The calculator uses Planck's constant h = 6.626 × 10⁻³⁴ J s.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of de Broglie wavelength?
A: The de Broglie wavelength determines the scale at which quantum effects become significant and helps explain phenomena like electron diffraction.

Q2: How does momentum affect wavelength?
A: Wavelength is inversely proportional to momentum - higher momentum results in shorter wavelength.

Q3: What is the relationship between energy and frequency?
A: Frequency is directly proportional to energy - higher energy results in higher frequency.

Q4: Can this be applied to all particles?
A: Yes, de Broglie's theory applies to all matter, though the effects are most noticeable for very small particles like electrons.

Q5: What are typical values for electron wavelength?
A: Electron wavelengths are typically on the order of picometers (10⁻¹² m), which is why electrons can be used in electron microscopes.