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:

• \( E \) — 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 photon energy is inversely proportional to its wavelength - shorter wavelengths correspond to higher 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 how photons will interact with matter.

4. Using the Calculator

Tips: Enter the wavelength in meters. For common light wavelengths, remember:

• Visible light: ~400-700 nm (4×10⁻⁷ to 7×10⁻⁷ m)
• X-rays: ~0.01-10 nm (1×10⁻¹¹ to 1×10⁻⁸ m)
• Radio waves: ~1 mm-100 km (1×10⁻³ to 1×10⁵ m)

5. Frequently Asked Questions (FAQ)

Q1: What is Planck's constant?
A: Planck's constant (h) is a fundamental physical constant that relates the energy of a photon to its frequency. Its value is approximately 6.626 × 10⁻³⁴ J·s.

Q2: Can I use this for any type of electromagnetic radiation?
A: Yes, this equation applies to all photons across the electromagnetic spectrum, from radio waves to gamma rays.

Q3: How can I convert the energy to electronvolts (eV)?
A: To convert joules to eV, divide the energy by the elementary charge (1.602 × 10⁻¹⁹ J/eV).

Q4: Why does shorter wavelength mean higher energy?
A: Because energy is inversely proportional to wavelength (E ∝ 1/λ). Shorter wavelength photons oscillate more rapidly, carrying more energy per quantum.

Q5: What's the relationship between this and E = hν?
A: Both equations calculate photon energy. E = hν uses frequency (ν), while E = hc/λ uses wavelength. They're equivalent since c = λν.