1. What is the Energy-Wavelength Equation?

The energy-wavelength equation \( E = \frac{h c}{\lambda} \) describes the relationship between the energy of a photon and its wavelength, where h is Planck's constant and c is the speed of light. This fundamental equation is used in quantum mechanics and spectroscopy.

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 physics, photochemistry, and optical engineering. It helps determine the energy levels of electromagnetic radiation.

4. Using the Calculator

Tips: Enter the wavelength in meters. The value must be positive and greater than zero. The calculator will compute the corresponding energy in Joules.

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 small is the energy calculated?
A: Photon energies are typically very small (on the order of 10⁻¹⁹ Joules), which is why we often use electronvolts (eV) in quantum physics.

Q3: Can I use other wavelength units?
A: Yes, but you must convert to meters first. Common conversions: 1 nm = 10⁻⁹ m, 1 μm = 10⁻⁶ m.

Q4: What is the relationship with frequency?
A: Since c = λν, the equation can also be written as E = hν, where ν is the frequency.

Q5: Why is this equation important?
A: It's fundamental to understanding quantum phenomena, photoelectric effect, and the particle nature of light.