1. What is the Energy-Wavelength Relationship?

The energy-wavelength relationship describes how the energy of a photon is inversely proportional to its wavelength. This fundamental principle in quantum mechanics connects the particle and wave properties of light.

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: Shorter wavelengths correspond to higher energy photons, while longer wavelengths correspond to lower energy photons.

3. Importance of Energy Calculation

Details: Calculating photon energy is essential in spectroscopy, quantum mechanics, 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. For best results, use scientific notation for very small wavelengths.

5. Frequently Asked Questions (FAQ)

Q1: What are typical energy values for visible light?
A: Visible light (400-700 nm) has photon energies of about 3.1-1.8 eV (5.0-2.9 × 10⁻¹⁹ J).

Q2: How does this relate to photon frequency?
A: Energy can also be calculated as E = h × ν, where ν is frequency. The two equations are connected by c = λ × ν.

Q3: What units should I use for wavelength?
A: The calculator requires meters, but common conversions are: 1 nm = 10⁻⁹ m, 1 Å = 10⁻¹⁰ m.

Q4: Can I calculate wavelength from energy?
A: Yes, simply rearrange the equation: λ = h × c / E.

Q5: Why is the energy value so small?
A: Individual photons carry very small amounts of energy. 1 J would be about 10¹⁸ visible light photons.