Electron Energy Wavelength Calculator

De Broglie Wavelength Formula:

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

Wavelength (λ):

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1. What is the De Broglie Wavelength?

The de Broglie wavelength is the wavelength associated with a particle and is related to its momentum. It demonstrates the wave-particle duality of matter, showing that particles like electrons exhibit wave-like properties.

2. How Does the Calculator Work?

The calculator uses the de Broglie wavelength formula:

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

Where:

\( \lambda \) — Wavelength (meters)
\( h \) — Planck's constant (6.626×10⁻³⁴ J·s)
\( m \) — Mass of the particle (kilograms)
\( E \) — Energy of the particle (joules)

Explanation: This formula calculates the wavelength of a particle given its mass and energy, based on the principles of quantum mechanics.

3. Importance of Wavelength Calculation

Details: Calculating the de Broglie wavelength is crucial in quantum mechanics for understanding particle behavior, electron microscopy, and various applications in modern physics and nanotechnology.

4. Using the Calculator

Tips: Enter the mass in kilograms and energy in joules. Both values must be positive numbers. For electrons, mass is approximately 9.109×10⁻³¹ kg.

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: Can this formula be used for any particle?
A: Yes, the de Broglie wavelength formula applies to all particles, though it's most significant for subatomic particles like electrons due to their small mass.

Q3: What are typical wavelength values for electrons?
A: Electron wavelengths typically range from 10⁻¹² to 10⁻⁹ meters, depending on their energy. Higher energy electrons have shorter wavelengths.

Q4: How is this related to electron microscopy?
A: The resolution of electron microscopes is limited by the wavelength of electrons. Shorter wavelengths allow for higher resolution imaging.

Q5: What are the limitations of this calculation?
A: This non-relativistic formula works well for particles at speeds much less than light speed. For relativistic particles, a modified formula is needed.