1. What is a Wavelength Frequency and Energy Calculator?

Definition: This calculator determines the frequency and energy of electromagnetic radiation based on its wavelength using Planck's equation and the wave equation.

Purpose: It helps physicists, chemists, and students understand the relationship between wavelength, frequency, and energy in electromagnetic waves.

2. How Does the Calculator Work?

The calculator uses two fundamental formulas:

Where:

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

Explanation: First, frequency is calculated from wavelength using the speed of light. Then energy is calculated by multiplying frequency by Planck's constant.

3. Importance of These Calculations

Details: These calculations are fundamental in quantum mechanics, spectroscopy, and understanding electromagnetic radiation from radio waves to gamma rays.

4. Using the Calculator

Tips: Enter the wavelength in meters (e.g., 500 nm = 5e-7 m), Planck's constant (default 6.626e-34 J·s), and speed of light (default 3e8 m/s). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What units should I use for wavelength?
A: The calculator expects wavelength in meters. Convert nanometers (1 nm = 10⁻⁹ m) or other units before input.

Q2: Why is Planck's constant important?
A: Planck's constant relates the energy of a photon to its frequency, a fundamental concept in quantum mechanics.

Q3: Can I calculate wavelength from frequency?
A: Yes, simply rearrange the equation: λ = c/f.

Q4: What's the practical application of these calculations?
A: Used in designing lasers, understanding atomic spectra, calculating photon energies in chemistry, and many physics applications.

Q5: How precise are these calculations?
A: Extremely precise when using accurate constants. The speed of light is exactly 299,792,458 m/s by definition.