De Broglie Wavelength Calculator With Kinetic Energy

De Broglie Wavelength Formula:

\[ \lambda = \frac{h}{\sqrt{2 m E}} \]

De Broglie Wavelength (λ):

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1. What is De Broglie Wavelength?

The de Broglie wavelength is a concept in quantum mechanics that states that every moving particle has an associated wavelength. It demonstrates the wave-particle duality of matter and is fundamental to understanding quantum behavior.

2. How Does the Calculator Work?

The calculator uses the de Broglie wavelength formula:

\[ \lambda = \frac{h}{\sqrt{2 m E}} \]

Where:

\( \lambda \) — De Broglie wavelength (meters)
\( h \) — Planck's constant (6.626 × 10⁻³⁴ J·s)
\( m \) — Mass of the particle (kilograms)
\( E \) — Kinetic energy of the particle (joules)

Explanation: The formula shows that wavelength decreases as mass or kinetic energy increases, meaning larger or faster-moving particles have shorter wavelengths.

3. Importance of De Broglie Wavelength

Details: De Broglie wavelength is crucial for understanding quantum phenomena such as electron diffraction, quantum tunneling, and the behavior of particles at atomic and subatomic scales.

4. Using the Calculator

Tips: Enter mass in kilograms and kinetic energy in joules. Both values must be positive numbers. For subatomic particles, use scientific notation (e.g., 9.11e-31 for electron mass).

5. Frequently Asked Questions (FAQ)

Q1: What is Planck's constant?
A: Planck's constant (h = 6.626 × 10⁻³⁴ J·s) is a fundamental constant in quantum mechanics that relates the energy of a photon to its frequency.

Q2: Why is de Broglie wavelength important?
A: It demonstrates that matter has wave-like properties, which is fundamental to quantum mechanics and explains phenomena like electron microscopy and quantum confinement.

Q3: What are typical de Broglie wavelength values?
A: For everyday objects, wavelengths are extremely small (undetectable). For electrons at typical energies, wavelengths are on the order of nanometers.

Q4: Can this formula be used for photons?
A: No, photons are massless particles. Their wavelength is calculated using E = hc/λ, where c is the speed of light.

Q5: What are the limitations of this formula?
A: The formula assumes non-relativistic speeds. For particles approaching the speed of light, relativistic corrections are needed.