1. What is the Energy-Wavelength Equation?

The energy-wavelength equation relates the energy of a photon to its wavelength using Planck's constant and the speed of light. This fundamental physics equation is crucial in quantum mechanics and electromagnetic theory.

2. How Does the Calculator Work?

The calculator uses the energy-wavelength equation:

Where:

• \( E \) — Energy in joules (J)
• \( h \) — Planck's constant (6.626 × 10⁻³⁴ J·s)
• \( c \) — Speed of light (3 × 10⁸ m/s)
• \( \lambda \) — Wavelength in meters (m)

Explanation: The equation shows that photon energy is inversely proportional to its wavelength - shorter wavelengths correspond to higher energy photons.

3. Importance of Energy Calculation

Details: Calculating photon energy is essential in spectroscopy, quantum physics, photochemistry, and understanding electromagnetic radiation across the spectrum from radio waves to gamma rays.

4. Using the Calculator

Tips: Enter wavelength in meters (e.g., 500 nm = 5e-7 m). The value must be positive and non-zero. The result is given in scientific notation for typical photon energies.

5. Frequently Asked Questions (FAQ)

Q1: What are typical photon energies?
A: Visible light photons have energies around 10⁻¹⁹ J (a few eV). X-rays are around 10⁻¹⁵ J (keV), while radio waves can be as low as 10⁻²⁵ J.

Q2: How does this relate to frequency?
A: The energy can also be calculated as E = h × f, where f is frequency. This is equivalent since c = λ × f.

Q3: Why is the result so small?
A: Individual photons carry very small amounts of energy. Macroscopic light contains enormous numbers of photons.

Q4: Can this be used for matter waves?
A: Yes, the de Broglie wavelength of particles follows a similar relationship using momentum instead of speed of light.

Q5: What about electron volts?
A: To convert to eV, divide the energy in joules by 1.602 × 10⁻¹⁹ J/eV.