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.

2. How Does the Calculator Work?

The calculator uses the energy-wavelength equation:

Where:

• \( E \) — Energy of photon (J)
• \( h \) — Planck's constant = 6.626×10⁻³⁴ J·s
• \( c \) — Speed of light = 3×10⁸ m/s
• \( \lambda \) — Wavelength (m)

Explanation: This equation shows that photon energy is inversely proportional to its wavelength - shorter wavelengths correspond to higher energy photons.

3. Importance of Energy Calculation

Details: Calculating photon energy is essential in quantum mechanics, spectroscopy, photochemistry, and understanding light-matter interactions across various scientific disciplines.

4. Using the Calculator

Tips: Enter wavelength in meters. The value must be valid (wavelength > 0). The calculator will compute the corresponding photon 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 is this equation used in practice?
A: It's used to calculate photon energy in spectroscopy, determine if light can trigger photochemical reactions, and understand energy levels in quantum systems.

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

Q4: What about frequency instead of wavelength?
A: The equation \( E = h\nu \) relates energy to frequency, where ν is frequency in Hz. This is equivalent since \( c = \lambda\nu \).

Q5: Why are the energy values so small?
A: Planck's constant is extremely small (6.626×10⁻³⁴ J·s), so individual photon energies are tiny. Macroscopic light involves enormous numbers of photons.