Electron Speed Calculator
Calculate electron speed from kinetic energy or accelerating voltage. Includes relativistic corrections, de Broglie wavelength, classical vs relativistic comparison.
Energy to Wavelength Calculator
Convert between photon energy and wavelength using E = hc/λ. Supports eV, joules, frequency, and nm inputs. Includes EM spectrum reference and common photon energies.
nm
Wavelength⧉
550.0000 nm
λ = hc/E — photon wavelength
Frequency⧉
545,090,909,090,909.0600 Hz
f = c/λ — oscillation frequency
Energy (eV)⧉
2.254540 eV
E = hf = hc/λ — single photon energy
Energy (J)⧉
0.0000 J
Energy in SI units (joules)
Wave Number⧉
18,181.82 cm⁻¹
1/λ in cm⁻¹ — used in spectroscopy
EM Spectrum Region⧉
Green
495–570 nm range
This photon is in the Green region of the electromagnetic spectrum.
Electromagnetic Spectrum Reference
| Region | Wavelength Range | Energy Range | Frequency Range |
|---|---|---|---|
| Gamma rays | 0.0001 nm – 0 nm | 124.0 keV – 12.4 MeV | 29,979,999,999,999,996,000.000 – 2,997,999,999,999,999,500,000.000 Hz |
| X-rays | 0.0100 nm – 10 nm | 123.9997 eV – 124.0 keV | 29,980,000,000,000,000.000 – 29,979,999,999,999,996,000.000 Hz |
| Ultraviolet | 10 nm – 380 nm | 3.2631 eV – 124.00 eV | 788,947,368,421,052.600 – 29,980,000,000,000,000.000 Hz |
| Violet | 380 nm – 450 nm | 2.7555 eV – 3.26 eV | 666,222,222,222,222.100 – 788,947,368,421,052.600 Hz |
| Blue | 450 nm – 495 nm | 2.5050 eV – 2.76 eV | 605,656,565,656,565.600 – 666,222,222,222,222.100 Hz |
| Green | 495 nm – 570 nm | 2.1754 eV – 2.51 eV | 525,964,912,280,701.700 – 605,656,565,656,565.600 Hz |
| Yellow | 570 nm – 590 nm | 2.1017 eV – 2.18 eV | 508,135,593,220,338.940 – 525,964,912,280,701.700 Hz |
| Orange | 590 nm – 620 nm | 2.0000 eV – 2.10 eV | 483,548,387,096,774.200 – 508,135,593,220,338.940 Hz |
| Red | 620 nm – 780 nm | 1.5897 eV – 2.00 eV | 384,358,974,358,974.300 – 483,548,387,096,774.200 Hz |
| Infrared | 780 nm – 1 mm | 0.0012 eV – 1.59 eV | 299,800,000,000.000 – 384,358,974,358,974.300 Hz |
| Microwave | 1 mm – 1 m | 0.0000 eV – 0.00 eV | 299,800,000.000 – 299,800,000,000.000 Hz |
| Radio | 1,000 mm – 1,000,000 m | 0.0000 eV – 0.00 eV | 299.800 – 299,800,000.000 Hz |
Common Photon Energies
| Source | λ (nm) | Energy (eV) | Frequency |
|---|---|---|---|
| AM Radio (1 MHz) | 300,000.00 mm | 0.0000 | 999,333.333 |
| FM Radio (100 MHz) | 3,000.00 mm | 0.0000 | 99,933,333.333 |
| Microwave oven (2.45 GHz) | 122.00 mm | 0.0000 | 2,457,377,049.180 |
| Infrared (10 μm) | 10,000.0 | 0.1240 | 29,979,999,999,999.996 |
| Red laser (632.8 nm) | 632.8 | 1.9595 | 473,767,383,059,418.440 |
| Green laser (532 nm) | 532.0 | 2.3308 | 563,533,834,586,466.100 |
| UV-A (365 nm) | 365.0 | 3.3973 | 821,369,863,013,698.600 |
| Medical X-ray | 0.050 | 24.80 keV | 5,995,999,999,999,999,000.000 |
| Gamma ray (Co-60) | 0.001 | 1.24 MeV | 299,799,999,999,999,930,000.000 |
Planning notes, formulas, and examples
About the Energy to Wavelength Calculator
Photon energy and wavelength are linked by the Planck-Einstein relation E = hc/λ, with h as Planck's constant and c as the speed of light. Shorter wavelengths mean higher photon energy, so ultraviolet, X-ray, and gamma-ray photons sit at the energetic end of the spectrum.
That relationship is central to spectroscopy, quantum mechanics, photochemistry, and radiation work. It is also the reason visible light, UV, microwaves, and radio waves behave so differently in real systems.
This calculator converts between wavelength, frequency, energy in joules, energy in electron volts, and wave number. It also labels the corresponding electromagnetic spectrum region so you can translate a value into the unit used by your field.
When This Page Helps
These conversions are common in optics, spectroscopy, atomic physics, and radio work, but the unit scales are awkward to do by hand. This calculator keeps the same photon value connected across wavelength, frequency, joules, electron volts, and wave number.
How to Use the Inputs
- Select the input mode: wavelength (nm), energy (eV), energy (J), or frequency (Hz).
- Enter the known value.
- Read all equivalent values: wavelength, frequency, energy in eV and joules, and wave number.
- Check which region of the electromagnetic spectrum the photon belongs to.
- Reference the EM spectrum table for ranges of all regions.
- Use preset buttons for common photon sources and wavelengths.
Formula used
Photon Energy: E = hf = hc/λ
Frequency: f = c/λ = E/h
Wavelength: λ = hc/E = c/f
Wave Number: k = 1/λ (in cm⁻¹)
Constants:
h = 6.626 × 10⁻³⁴ J·s
c = 2.998 × 10⁸ m/s
1 eV = 1.602 × 10⁻¹⁹ J
hc = 1240 eV·nm (useful shortcut)Example Calculation
Result: 2.254 eV
Green light at 550 nm: E = hc/λ = (6.626×10⁻³⁴ × 2.998×10⁸)/(550×10⁻⁹) = 3.61×10⁻¹⁹ J = 2.254 eV. The frequency is f = c/λ = 5.45×10¹⁴ Hz.
Tips & Best Practices
- Quick conversion: E(eV) ≈ 1240/λ(nm). For 500 nm green light: 1240/500 = 2.48 eV.
- Visible light spans roughly 380-780 nm, corresponding to 1.6-3.3 eV.
- The energy to break a C-C bond is about 3.6 eV (345 nm, UV range) — this is why UV causes chemical damage.
- Room temperature thermal energy (kT at 300 K) is about 0.026 eV, corresponding to ~48 μm infrared.
- Medical X-rays typically use 20-150 keV photons (0.008-0.06 nm wavelengths).
- The cosmic microwave background has peak wavelength of about 1.06 mm, corresponding to photon energy of 1.2 meV.
The Planck-Einstein Relation
When Max Planck proposed in 1900 that electromagnetic energy is exchanged in discrete quanta of E = hf, he launched the quantum revolution. Einstein extended this in 1905 to argue that light itself consists of particles (photons) each carrying energy E = hf. This dual wave-particle nature of light resolved paradoxes like the photoelectric effect and ultraviolet catastrophe.
The relation E = hc/λ is simply E = hf combined with c = fλ. It means every photon has a definite energy determined by its wavelength (or equivalently, frequency). This discreteness is what makes quantum mechanics fundamentally different from classical physics.
Spectroscopy and Chemical Analysis
The energy-wavelength relationship is the foundation of spectroscopy — the study of how matter absorbs, emits, and scatters light. Each chemical element and molecule has a unique set of energy levels, producing characteristic spectral lines. By measuring which wavelengths are absorbed or emitted, scientists can identify substances, determine chemical compositions, and probe molecular structures.
Infrared spectroscopy uses wave numbers (cm⁻¹) as the standard unit because the positions of molecular vibration absorption bands fall at convenient numbers: C-H stretches near 3000 cm⁻¹, C=O stretches near 1700 cm⁻¹, and so on.
From Radio to Gamma Rays
The electromagnetic spectrum spans over 20 orders of magnitude in wavelength and energy. Radio waves (wavelengths of meters to kilometers, energies of nano-eV) carry broadcast signals. Microwaves (mm to cm, μeV to meV) heat food and enable wireless communication. Infrared (μm, tenths of eV) is felt as radiant heat. Visible light (400-700 nm, 1.8-3.1 eV) is the narrow window our eyes evolved to detect. Ultraviolet (nm, eV) causes sunburn. X-rays (pm to nm, keV) penetrate tissue for medical imaging. Gamma rays (sub-pm, MeV to GeV) are emitted by nuclear reactions and cosmic events.
Sources & Methodology
Last updated:
Frequently Asked Questions
Because E = hc/λ. As energy goes up, wavelength goes down, so the two move in opposite directions.
An electron volt is the energy gained by one electron moving through one volt, equal to 1.602 × 10⁻¹⁹ joules. It is a common unit in atomic and particle physics.
The constant hc is convenient in photon work because it lets you estimate energy quickly with E(eV) ≈ 1240/λ(nm). That is handy for visible and UV light.
Wave number is the reciprocal of wavelength, usually written in cm⁻¹. It is common in infrared spectroscopy because many molecular bands are tabulated that way.
Only photons above the relevant ionization threshold can remove electrons. For most atoms that means UV or shorter wavelengths, not visible light or radio.
The photoelectric effect showed that light arrives in discrete photons. If a photon has enough energy to exceed a metal’s work function, it can eject an electron.
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