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 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 for understanding atomic transitions, photoelectric effect, spectroscopy, and various applications in physics, chemistry, and engineering.

4. Using the Calculator

Tips: Enter wavelength in meters. The value must be positive and greater than zero. For nanometer inputs, convert to meters (1 nm = 10⁻⁹ m).

5. Frequently Asked Questions (FAQ)

Q1: What are typical wavelength values for visible light?
A: Visible light wavelengths range from approximately 380 nm (violet) to 750 nm (red), which is 3.8×10⁻⁷ m to 7.5×10⁻⁷ m.

Q2: How does energy relate to frequency?
A: Energy is directly proportional to frequency: E = hν, where ν is frequency. Since c = λν, the equations are equivalent.

Q3: What are common units for photon energy?
A: While joules are the SI unit, electronvolts (eV) are commonly used in atomic physics (1 eV = 1.602×10⁻¹⁹ J).

Q4: Why is Planck's constant important?
A: Planck's constant is a fundamental physical constant that relates the energy of photons to their frequency, forming the basis of quantum mechanics.

Q5: Can this equation be used for all electromagnetic radiation?
A: Yes, this equation applies to all photons across the electromagnetic spectrum, from radio waves to gamma rays.