1. What is the Energy-Wavelength Equation?

The energy-wavelength equation \( E = \frac{h \cdot c}{\lambda} \) relates the energy of a photon to its wavelength, where h is Planck's constant and c is the speed of light. This fundamental equation in quantum mechanics describes the energy carried by electromagnetic radiation.

2. How Does the Calculator Work?

The calculator uses the energy-wavelength equation:

Where:

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

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

3. Importance of Energy Calculation

Details: Calculating photon energy is essential in various fields including spectroscopy, quantum mechanics, photochemistry, and optical engineering. It helps determine the behavior of light-matter interactions.

4. Using the Calculator

Tips: Enter the wavelength in meters. For common wavelengths, remember that 1 nanometer = 10⁻⁹ meters. The wavelength must be greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What are typical wavelength values?
A: Visible light ranges from 380-750 nm (3.8×10⁻⁷ to 7.5×10⁻⁷ m), while X-rays are around 10⁻¹⁰ to 10⁻⁸ m.

Q2: How is this related to photon frequency?
A: The equation can also be written as E = h·ν, where ν is frequency, since c = λ·ν.

Q3: What are typical energy values for photons?
A: Visible light photons have energies around 10⁻¹⁹ J, while X-ray photons can have energies around 10⁻¹⁵ J.

Q4: Why is the energy so small?
A: Planck's constant is very small (6.626×10⁻³⁴ J·s), so individual photon energies are tiny on human scales.

Q5: Can this be used for all electromagnetic radiation?
A: Yes, this equation applies to all photons across the electromagnetic spectrum.