Frequency Wavelength Photon Energy Calculator

What is Frequency, Wavelength, and Photon Energy?

Frequency, wavelength, and photon energy are fundamental concepts in quantum physics and electromagnetic theory. Frequency (f) is the number of wave cycles that pass a fixed point per unit of time. Wavelength (λ) is the distance between two consecutive crests or troughs of a wave. Photon energy (E) is the amount of energy carried by a single photon, which is the elementary particle of light and all other forms of electromagnetic radiation.

Formulas

The relationships between frequency, wavelength, and photon energy are expressed by the following equations:

\[ c = f \lambda \]

\[ E = hf = \frac{hc}{\lambda} \]

Where:

• c is the speed of light in vacuum (approximately 3 × 10⁸ m/s)
• f is the frequency (measured in Hz)
• λ (lambda) is the wavelength (measured in meters)
• E is the photon energy (measured in joules, J)
• h is Planck's constant (approximately 6.626 × 10⁻³⁴ J·s)

Calculation Steps

Let's calculate the photon energy of a light wave with a frequency of 5 × 10¹⁴ Hz:

1. Identify the known values:
   • f = 5 × 10¹⁴ Hz
   • h ≈ 6.626 × 10⁻³⁴ J·s
2. Apply the photon energy formula: \[ E = hf \]
3. Substitute the known values: \[ E = (6.626 \times 10^{-34} \text{ J·s})(5 \times 10^{14} \text{ Hz}) \]
4. Perform the calculation: \[ E = 3.313 \times 10^{-19} \text{ J} \]

Example and Visual Representation

Let's visualize the relationship between frequency, wavelength, and photon energy:

This visual representation shows:

• The wave nature of light, represented by the sinusoidal curve (blue)
• The wavelength (λ), which is the distance between two consecutive peaks
• The frequency (f), represented by the number of wave cycles per unit time (green)
• The photon energy (E), which is proportional to the frequency (red)