Calculate photon energy from frequency (E = hf) or wavelength (E = hc/λ). Free online quantum physics calculator with Planck's constant and speed of light.
Calculate photon energy from frequency or wavelength using E = hf or E = hc/λ
Formula:
E = hf
Where: E = photon energy, h = Planck's constant (6.626 × 10⁻³⁴ J·s), f = frequency
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Photon energy is a fundamental concept in quantum physics, representing the energy carried by a single photon of electromagnetic radiation. Photons are the quantum particles of light and all electromagnetic radiation, and their energy is directly related to their frequency and wavelength. Our Photon Energy Calculator makes it easy to calculate photon energy using two formulas: E = hf (from frequency) or E = hc/λ (from wavelength), where h is Planck's constant and c is the speed of light.
Understanding photon energy is essential for fields ranging from quantum mechanics and optics to spectroscopy, photovoltaics, and medical imaging. The energy of a photon determines its ability to interact with matter, making it crucial for understanding atomic transitions, chemical reactions, and the photoelectric effect.
Our Photon Energy Calculator offers two calculation modes:
Simply select your calculation mode, enter the required value (leave one empty to calculate), choose your units, and click Calculate to get instant results with step-by-step solutions. You can also calculate frequency or wavelength from a known photon energy.
Photon energy can be calculated using different formulas depending on available information:
E = hf
Where: E = photon energy, h = Planck's constant (6.626 × 10⁻³⁴ J·s), f = frequency
This formula directly relates photon energy to frequency. Higher frequency photons have more energy, which is why gamma rays are more energetic than radio waves.
E = hc / λ
Where: E = photon energy, h = Planck's constant, c = speed of light (2.998 × 10⁸ m/s), λ = wavelength
This formula relates photon energy to wavelength. Since c = fλ, we can substitute to get E = hc/λ. Shorter wavelengths correspond to higher energy photons.
Photon energy calculations are used in numerous scientific and technological applications:
Photon energy calculations use various units depending on the application:
Common Values:
Calculate the energy of a photon with wavelength 550 nm (green light).
λ = 550 nm = 5.5 × 10⁻⁷ m
E = hc/λ = (6.626 × 10⁻³⁴ J·s × 2.998 × 10⁸ m/s) / (5.5 × 10⁻⁷ m)
E = 3.61 × 10⁻¹⁹ J = 2.25 eV
Calculate the energy of an X-ray photon with wavelength 0.1 nm.
λ = 0.1 nm = 1 × 10⁻¹⁰ m
E = hc/λ = (6.626 × 10⁻³⁴ × 2.998 × 10⁸) / (1 × 10⁻¹⁰)
E = 1.986 × 10⁻¹⁵ J = 12,400 eV = 12.4 keV
Calculate the energy of a photon with frequency 5 × 10¹⁴ Hz (visible light).
f = 5 × 10¹⁴ Hz
E = hf = (6.626 × 10⁻³⁴ J·s) × (5 × 10¹⁴ Hz)
E = 3.313 × 10⁻¹⁹ J = 2.07 eV
For visible light, a quick approximation: E(eV) ≈ 1240 / λ(nm)
For λ = 620 nm (red light):
E ≈ 1240 / 620 = 2.0 eV
The electromagnetic spectrum spans a wide range of photon energies:
Higher energy photons can ionize atoms, break chemical bonds, and penetrate matter more effectively. This is why X-rays and gamma rays are used in medical imaging and why UV light can cause skin damage.
The photoelectric effect demonstrates the particle nature of light and the importance of photon energy:
A photon is a quantum particle of light and all electromagnetic radiation. It has zero rest mass, travels at the speed of light, and carries energy proportional to its frequency. Photons exhibit both wave-like and particle-like properties (wave-particle duality).
Photon energy is directly proportional to frequency (E = hf) and inversely proportional to wavelength (E = hc/λ). Higher frequency or shorter wavelength photons have more energy. This is why gamma rays are more energetic than radio waves.
Planck's constant (h = 6.626 × 10⁻³⁴ J·s) is a fundamental constant in quantum mechanics that relates the energy of a photon to its frequency. It was discovered by Max Planck and is fundamental to quantum theory.
The electron volt is convenient for atomic and subatomic physics because it's on the same scale as atomic energy levels. 1 eV is the energy gained by an electron accelerated through 1 volt. Many atomic transitions are in the eV range, making it more practical than joules for these calculations.
Yes! From energy, you can calculate frequency using f = E/h, or wavelength using λ = hc/E. Our calculator supports calculating any of these three quantities when you know the other two.
In visible light, different photon energies correspond to different colors. Red light (longer wavelength, ~620-750 nm) has lower energy (~1.65-2.0 eV), while violet light (shorter wavelength, ~380-450 nm) has higher energy (~2.75-3.26 eV). The energy determines the color we perceive.
Understanding photon energy is fundamental to quantum physics, optics, and modern technology. Our Photon Energy Calculator simplifies these calculations, supporting multiple calculation modes and units to make determining photon energy, frequency, and wavelength easy and accurate.
Ready to explore more quantum and wave concepts? Check out our Wavelength Calculator for wave properties, our Frequency Calculator for frequency calculations, or our Wavelength to Frequency Calculator for conversions.
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