1. What is the Wavelength Formula?

The wavelength formula λ = hc/E calculates the wavelength of a photon from its energy, where h is Planck's constant, c is the speed of light, and E is the photon energy. This relationship is fundamental in quantum mechanics and electromagnetic theory.

2. How Does the Calculator Work?

The calculator uses the wavelength formula:

Where:

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

Explanation: The formula shows the inverse relationship between photon energy and wavelength - higher energy photons have shorter wavelengths.

3. Importance of Wavelength Calculation

Details: Calculating wavelength from photon energy is essential in spectroscopy, quantum physics, telecommunications, and understanding the electromagnetic spectrum. It helps determine the type of electromagnetic radiation (radio, microwave, infrared, visible light, UV, X-ray, or gamma ray).

4. Using the Calculator

Tips: Enter photon energy in joules. The value must be positive and non-zero. For very small energies typical of photons, you may need to use scientific notation (e.g., 4.0e-19 for 4.0 × 10⁻¹⁹).

5. Frequently Asked Questions (FAQ)

Q1: What are typical photon energy values?
A: Photon energies vary widely: radio waves (~10⁻²⁴ J), visible light (~10⁻¹⁹ J), X-rays (~10⁻¹⁵ J), and gamma rays (>10⁻¹³ J).

Q2: Can I use electronvolts instead of joules?
A: Yes, but you'll need to convert first (1 eV = 1.602 × 10⁻¹⁹ J). Many physics applications use eV as the standard unit for photon energy.

Q3: What is the relationship between wavelength and color?
A: For visible light: violet (~400 nm) to red (~700 nm). Shorter wavelengths correspond to higher energies and bluer colors.

Q4: Why is Planck's constant important?
A: Planck's constant is a fundamental physical constant that relates the energy of a photon to its frequency (E = hf), forming the basis of quantum mechanics.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the well-established constants h and c. Accuracy depends on the precision of your energy measurement.