De Broglie Wavelength Calculator With Time

De Broglie Wavelength Equation:

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

De Broglie Wavelength (λ):

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1. What is the De Broglie Wavelength?

The De Broglie wavelength is the wavelength associated with a moving particle, demonstrating wave-particle duality. It shows that matter has wave-like properties, with the wavelength inversely proportional to the particle's momentum.

2. How Does the Calculator Work?

The calculator uses the De Broglie equation:

\[ \lambda = \frac{h}{p} = \frac{h}{m \times v} \]

Where:

\( \lambda \) — Wavelength (meters)
\( h \) — Planck's constant (6.626 × 10⁻³⁴ J·s)
\( p \) — Momentum (kg·m/s)
\( m \) — Mass (kg)
\( v \) — Velocity (m/s)

Explanation: The equation shows that as momentum increases (either through mass or velocity), the wavelength decreases.

3. Importance of Wavelength Calculation

Details: Calculating De Broglie wavelengths is crucial in quantum mechanics, electron microscopy, and understanding the wave nature of particles. It helps explain phenomena like electron diffraction.

4. Using the Calculator

Tips: Enter mass in kilograms and velocity in meters per second. Both values must be positive numbers. For subatomic particles, use very small mass values (e.g., electron mass = 9.11 × 10⁻³¹ kg).

5. Frequently Asked Questions (FAQ)

Q1: Why is time not directly in the equation?
A: Time is indirectly involved through velocity (distance/time), but the fundamental relationship is between wavelength and momentum.

Q2: What are typical De Broglie wavelength values?
A: For macroscopic objects, wavelengths are extremely small (undetectable). For electrons at typical velocities, wavelengths are comparable to atomic sizes.

Q3: When is this concept important?
A: Crucial in quantum mechanics experiments, electron microscopy, and any situation where wave-particle duality is significant.

Q4: Are there limitations to this equation?
A: The equation is non-relativistic. For particles approaching light speed, relativistic corrections are needed.

Q5: Can this be observed in everyday objects?
A: For everyday objects, the wavelength is so small it's effectively undetectable. Wave nature becomes significant only for very small particles like electrons.