De Broglie Wavelength Calculator

De Broglie Equation:

\[ \lambda = \frac{h}{p} \]

Wavelength (λ):

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1. What is the De Broglie Wavelength?

The De Broglie wavelength is a concept in quantum mechanics that states all matter exhibits wave-like properties. It is named after French physicist Louis de Broglie, who proposed that particles of matter also have wave characteristics.

2. How Does the Calculator Work?

The calculator uses the De Broglie equation:

\[ \lambda = \frac{h}{p} \]

Where:

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

Explanation: The equation shows the inverse relationship between a particle's momentum and its wavelength - higher momentum results in shorter wavelength.

3. Importance of De Broglie Wavelength

Details: The concept of matter waves was fundamental to the development of quantum mechanics and explains phenomena like electron diffraction. It demonstrates the wave-particle duality of matter.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is Planck's constant?
A: Planck's constant (h) is a fundamental physical constant that relates the energy of a photon to its frequency. Its value is approximately 6.626 × 10⁻³⁴ joule-seconds.

Q2: How is momentum calculated?
A: Momentum (p) is calculated as the product of mass (m) and velocity (v): p = m × v. For this calculator, you need to provide the momentum value directly.

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

Q4: 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.

Q5: What experimental evidence supports matter waves?
A: The Davisson-Germer experiment in 1927 demonstrated that electrons show diffraction patterns when scattered by crystals, confirming their wave-like nature.