de Broglie Wavelength Calculator with Frequency Table

de Broglie Wavelength Formula:

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

Wavelength (λ):

1. What is de Broglie Wavelength?

Definition: The de Broglie wavelength is the wavelength associated with a moving particle, demonstrating wave-particle duality in quantum mechanics.

Purpose: This calculator helps determine the quantum wavelength of particles with mass, showing their wave-like properties.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( \lambda \) — de Broglie wavelength (meters)
\( h \) — Planck's constant (6.626 × 10⁻³⁴ J·s)
\( m \) — Mass of the particle (kilograms)
\( v \) — Velocity of the particle (meters/second)

3. Typical Wavelength Examples

Object	Mass (kg)	Velocity (m/s)	Wavelength (m)
Electron (1eV)	9.11 × 10⁻³¹	5.93 × 10⁵	1.23 × 10⁻⁹
Baseball	0.145	40	1.14 × 10⁻³⁴
Person walking	70	1	9.47 × 10⁻³⁶

4. Using the Calculator

Tips: Enter the mass in kilograms and velocity in meters/second. Both values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: Why is the wavelength so small for macroscopic objects?
A: Because Planck's constant is extremely small, and macroscopic objects have relatively large mass and velocity.

Q2: What's the significance of de Broglie wavelength?
A: It demonstrates that matter has wave properties, fundamental to quantum mechanics and explaining phenomena like electron diffraction.

Q3: How is this related to the Heisenberg Uncertainty Principle?
A: The wave nature of particles leads to fundamental limits in simultaneously measuring position and momentum.

Q4: Can we observe these wavelengths in everyday objects?
A: No, for everyday objects the wavelengths are far too small to detect. They're only significant for very small particles like electrons.

Q5: How does this relate to electron microscopes?
A: Electron microscopes use the wave nature of electrons (with wavelengths much shorter than visible light) to achieve higher resolution.