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De Broglie Wavelength Equation:
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The De Broglie wavelength equation describes the wave nature of matter, showing that particles like electrons exhibit wave-like properties. It was proposed by Louis de Broglie in 1924 and is fundamental to quantum mechanics.
The calculator uses the De Broglie wavelength equation:
Where:
Explanation: The equation shows that the wavelength of a particle is inversely proportional to its momentum (mass × velocity).
Details: Calculating De Broglie wavelength is crucial for understanding quantum behavior, electron microscopy, and wave-particle duality experiments. It helps predict when quantum effects become significant.
Tips: Enter mass in kilograms and velocity in meters per second. For subatomic particles, use very small mass values (e.g., electron mass = 9.109 × 10⁻³¹ kg).
Q1: Why is Planck's constant in the equation?
A: Planck's constant relates the energy of a photon to its frequency, and in this context, it connects the particle properties (mass, velocity) with wave properties (wavelength).
Q2: What's a typical wavelength for an electron?
A: For an electron with 1 eV energy (velocity ~593 km/s), λ ≈ 1.23 nm - comparable to atomic spacing in crystals, explaining electron diffraction patterns.
Q3: Does this apply to macroscopic objects?
A: Yes, but wavelengths are extremely small. A 1 kg object moving at 1 m/s has λ ≈ 6.6 × 10⁻³⁴ m - far too small to observe wave effects.
Q4: How was this equation verified experimentally?
A: Davisson-Germer experiment (1927) showed electron diffraction from nickel crystals, confirming wave nature with wavelengths matching de Broglie's prediction.
Q5: What about relativistic particles?
A: For particles approaching light speed, use relativistic momentum \( p = \gamma m v \) where \( \gamma \) is the Lorentz factor.