De Broglie Wavelength Given Total Energy Calculator

De Broglie Wavelength Formula:

\[ \lambda_{TE} = \frac{[hP]}{\sqrt{2 \times M \times (E_{radiated} - PE)}} \]

De Broglie Wavelength:

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1. What is De Broglie Wavelength?

The De Broglie wavelength is a concept in quantum mechanics that states all matter exhibits wave-like properties. It represents the wavelength associated with a particle and is inversely proportional to its momentum.

2. How Does the Calculator Work?

The calculator uses the De Broglie wavelength formula:

\[ \lambda_{TE} = \frac{[hP]}{\sqrt{2 \times M \times (E_{radiated} - PE)}} \]

Where:

\( \lambda_{TE} \) — De Broglie wavelength (m)
\( [hP] \) — Planck constant (6.626070040 × 10⁻³⁴ J·s)
\( M \) — Mass in kilograms
\( E_{radiated} \) — Total energy radiated (W/m²)
\( PE \) — Potential energy (J)

Explanation: The formula calculates the wavelength of a particle based on its mass and the difference between total radiated energy and potential energy.

3. Importance of De Broglie Wavelength

Details: De Broglie wavelength is fundamental in quantum mechanics, explaining wave-particle duality and enabling technologies like electron microscopy and quantum computing.

4. Using the Calculator

Tips: Enter mass in Dalton, total energy radiated in W/m², and potential energy in J. All values must be positive, and energy radiated should be greater than potential energy.

5. Frequently Asked Questions (FAQ)

Q1: What is wave-particle duality?
A: Wave-particle duality is the concept that every particle or quantum entity exhibits both wave and particle properties.

Q2: Why is mass converted from Dalton to kilograms?
A: The formula requires mass in SI units (kilograms) for consistent dimensional analysis with other SI units in the equation.

Q3: What are typical De Broglie wavelength values?
A: For macroscopic objects, wavelengths are extremely small (undetectable). For subatomic particles, wavelengths can be significant and measurable.

Q4: When is this formula applicable?
A: This formula applies to non-relativistic particles where the energy difference is properly defined and measurable.

Q5: What are practical applications of De Broglie wavelength?
A: Electron microscopy, neutron diffraction, quantum tunneling devices, and fundamental research in quantum mechanics.