Photon Energy Calculator Based on Wavelength

Calculating the energy of a photon based on its wavelength is a fundamental tool in physics, chemistry, and optics. This calculator provides quick conversions for wavelengths like 990 nm, outputting energy in both electronvolts (eV) and joules (J).

Historical Background

The relationship between a wave’s energy and its wavelength stems from quantum mechanics, pioneered by Max Planck and Albert Einstein in the early 20th century. Planck’s work on blackbody radiation and Einstein’s explanation of the photoelectric effect established that light consists of photons, each carrying energy inversely proportional to its wavelength.

Calculation Formula

The energy of a photon is calculated using:

• Energy in Joules:
  \[ E = \frac{h \cdot c}{\lambda} \] Where:

  • \( h = 6.62607015 \times 10^{-34} \, \text{J·s} \) (Planck’s constant)
  • \( c = 2.99792458 \times 10^8 \, \text{m/s} \) (speed of light)
  • \( \lambda \) = wavelength in meters

• Energy in eV:
  \[ E_{\text{eV}} = \frac{E_{\text{Joules}}}{1.60217662 \times 10^{-19}} \]

Example Calculation

For a wavelength of 990 nm (\( 990 \times 10^{-9} \, \text{m} \)):

• Energy in Joules:
  \[ E = \frac{6.62607015 \times 10^{-34} \cdot 2.99792458 \times 10^8}{990 \times 10^{-9}} \approx 2.007 \times 10^{-19} \, \text{J} \]
• Energy in eV:
  \[ E_{\text{eV}} = \frac{2.007 \times 10^{-19}}{1.60217662 \times 10^{-19}} \approx 1.252 \, \text{eV} \]

Importance and Usage Scenarios

Photon energy calculations are vital in:

• Spectroscopy, to identify materials based on emitted or absorbed light.
• Photovoltaics, for designing solar cells responsive to specific wavelengths.
• Medical imaging and laser technology, where precise energy levels determine effectiveness.

Common FAQs

1. What does nm stand for in wavelength?

   • "nm" means nanometers, equal to \( 10^{-9} \) meters, commonly used for visible and near-infrared light.

2. Why are there two energy outputs?

   • Joules is the SI unit, while eV (electronvolts) is widely used in physics and chemistry for atomic-scale energy levels.

3. What type of wave does this apply to?

   • This calculator assumes electromagnetic waves (e.g., light), where the photon energy formula applies directly.

This tool simplifies photon energy calculations, making it accessible for students, researchers, and professionals working with electromagnetic radiation.