1. What is the Photon Energy Equation?

The photon energy equation \( E = \frac{hc}{\lambda} \) relates the energy of a photon to its wavelength, where h is Planck's constant and c is the speed of light. This fundamental equation in quantum mechanics describes the particle-like properties of light.

2. How Does the Calculator Work?

The calculator uses the photon energy equation:

Where:

• \( E \) — Photon energy (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 shorter wavelengths correspond to higher energy photons, while longer wavelengths correspond to lower energy photons.

3. Importance of Photon Energy Calculation

Details: Calculating photon energy is essential in fields like quantum physics, spectroscopy, photochemistry, and optical engineering. It helps determine the interaction of light with matter.

4. Using the Calculator

Tips: Enter the wavelength in meters (for example, visible light is about 400-700 nm or 4.0-7.0 × 10⁻⁷ m). The calculator will output the photon energy in joules.

5. Frequently Asked Questions (FAQ)

Q1: How do I convert nanometers to meters?
A: 1 nanometer = 10⁻⁹ meters. So 500 nm = 500 × 10⁻⁹ = 5.0 × 10⁻⁷ meters.

Q2: What is the energy range for visible light?
A: Approximately 1.8 eV (red) to 3.1 eV (violet), or 2.88 × 10⁻¹⁹ J to 4.97 × 10⁻¹⁹ J.

Q3: Can I calculate wavelength from energy?
A: Yes, by rearranging the equation: \( \lambda = \frac{hc}{E} \).

Q4: Why is the energy so small in joules?
A: Individual photons carry very small amounts of energy. In practical applications, we typically deal with large numbers of photons.

Q5: How does this relate to the photoelectric effect?
A: The equation explains why only light above a certain frequency (short enough wavelength) can eject electrons from a material - the photon must have sufficient energy.