1. What is the Planck-Einstein Relation?

The Planck-Einstein relation describes the energy of a photon in terms of its wavelength. This fundamental equation in quantum mechanics connects the particle and wave properties of light.

2. How Does the Calculator Work?

The calculator uses the Planck-Einstein relation:

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 of the photon (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 understanding electromagnetic radiation interactions with matter.

4. Using the Calculator

Tips: Enter wavelength in meters. The value must be positive and non-zero. For common wavelengths, remember that 1 nm = 10⁻⁹ m.

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). X-rays are around 10⁻¹⁰ m, while radio waves can be meters long.

Q2: How does energy relate to frequency?
A: Energy can also be calculated as E = hν, where ν is frequency. Since c = λν, both formulas are equivalent.

Q3: What are typical energy values for photons?
A: Visible light photons have energies around 10⁻¹⁹ J. Higher energy photons (X-rays, gamma rays) have smaller wavelengths and higher energies.

Q4: Can this calculator handle very small wavelengths?
A: Yes, but extremely small wavelengths may produce very large energy values that could exceed typical display precision.

Q5: What are practical applications of this calculation?
A: Used in designing lasers, understanding atomic spectra, medical imaging (X-rays), astronomy, and photovoltaic cell design.