eV/c² to kg Converter
Precise particle physics mass conversion from electronvolt per c-squared to kilogram
Mass Converter
Input:
Scientific Notation:
Conversion Factor: 1 eV/c² = 1.782661921 × 10⁻³⁶ kg
Explanation:
Common Conversions
| eV/c² Value | Kilogram (kg) | Scientific Notation |
|---|---|---|
| 1 eV/c² | 0.000000000000000000000000000000000001782661921 kg | 1.783 × 10⁻³⁶ kg |
| 1 keV/c² | 1.783 × 10⁻³³ kg | 1.783 × 10⁻³³ kg |
| 1 MeV/c² | 1.783 × 10⁻³⁰ kg | 1.783 × 10⁻³⁰ kg |
| 1 GeV/c² | 1.783 × 10⁻²⁷ kg | 1.783 × 10⁻²⁷ kg |
| 1 TeV/c² | 1.783 × 10⁻²⁴ kg | 1.783 × 10⁻²⁴ kg |
| 511 keV/c² (electron) | 9.109 × 10⁻³¹ kg | 9.109 × 10⁻³¹ kg |
| 938.3 MeV/c² (proton) | 1.673 × 10⁻²⁷ kg | 1.673 × 10⁻²⁷ kg |
| 939.6 MeV/c² (neutron) | 1.675 × 10⁻²⁷ kg | 1.675 × 10⁻²⁷ kg |
| 125.1 GeV/c² (Higgs boson) | 2.230 × 10⁻²⁵ kg | 2.230 × 10⁻²⁵ kg |
Conversion Formula and Steps
The fundamental relationship derives from Einstein’s mass-energy equivalence:
Rearranging for mass:
Conversion formula:
Step-by-Step Conversion Method
- Identify your energy value in electronvolts (eV, keV, MeV, GeV, etc.)
- Convert to base eV if in different scale (e.g., 1 MeV = 10⁶ eV)
- Multiply by the conversion factor: 1.782661921 × 10⁻³⁶ kg per eV
- Express result in appropriate scientific notation for clarity
- Verify the order of magnitude matches expected particle mass ranges
Example Conversion
Convert 938.3 MeV/c² (proton mass) to kilograms:
1. Start with: 938.3 MeV/c²
2. Convert to eV: 938.3 × 10⁶ eV/c² = 9.383 × 10⁸ eV/c²
3. Apply conversion: 9.383 × 10⁸ × 1.782661921 × 10⁻³⁶ kg
4. Result: 1.673 × 10⁻²⁷ kg
Scientific Notation Scales
eV/c² (electronvolt)
Scale: Base unit
Typical particles: Low-energy neutrinos
Order: 10⁰ eV
keV/c² (kiloelectronvolt)
Scale: 10³ eV
Typical particles: X-ray photons, electron mass (511 keV/c²)
Order: 10³ eV
MeV/c² (megaelectronvolt)
Scale: 10⁶ eV
Typical particles: Protons, neutrons, pions
Order: 10⁶ eV
GeV/c² (gigaelectronvolt)
Scale: 10⁹ eV
Typical particles: Heavy quarks, Z boson, Higgs boson
Order: 10⁹ eV
TeV/c² (teraelectronvolt)
Scale: 10¹² eV
Typical particles: Hypothetical heavy particles
Order: 10¹² eV
Particle Physics Context
Why eV/c² Matters
In particle physics, eV/c² serves as the standard unit for expressing particle masses. This notation directly reflects Einstein’s mass-energy equivalence principle (E = mc²), making it natural to describe mass in terms of energy divided by the speed of light squared. When physicists say an electron has a mass of 511 keV/c², they’re referencing the energy equivalent of that mass.
Mass-Energy Equivalence
Einstein’s famous equation E = mc² reveals that mass and energy are interchangeable. In particle accelerators and high-energy physics experiments, this relationship becomes critical. Particles can be created from pure energy, and their masses are most conveniently expressed in energy units. The conversion to kilograms connects these quantum-scale measurements to the SI system used in everyday physics.
Fundamental Particles
| Particle | Mass (eV/c²) | Mass (kg) | Category |
|---|---|---|---|
| Electron | 511 keV/c² | 9.109 × 10⁻³¹ kg | Lepton |
| Muon | 105.7 MeV/c² | 1.884 × 10⁻²⁸ kg | Lepton |
| Proton | 938.3 MeV/c² | 1.673 × 10⁻²⁷ kg | Baryon |
| Neutron | 939.6 MeV/c² | 1.675 × 10⁻²⁷ kg | Baryon |
| W Boson | 80.4 GeV/c² | 1.433 × 10⁻²⁵ kg | Gauge Boson |
| Z Boson | 91.2 GeV/c² | 1.626 × 10⁻²⁵ kg | Gauge Boson |
| Higgs Boson | 125.1 GeV/c² | 2.230 × 10⁻²⁵ kg | Scalar Boson |
| Top Quark | 173.1 GeV/c² | 3.086 × 10⁻²⁵ kg | Quark |
Historical Development
The electronvolt emerged as a natural unit in atomic and nuclear physics during the early 20th century. As physicists probed deeper into atomic structure, they found it convenient to measure energies in terms of the voltage needed to accelerate electrons. The unit gained prominence through the work of Robert Millikan and others studying the photoelectric effect and atomic spectra.
With Einstein’s 1905 publication of special relativity and E = mc², the connection between energy and mass became fundamental. By the 1930s, as particle accelerators developed, expressing particle masses in eV/c² became standard practice. This notation proved especially useful at facilities like the Cavendish Laboratory and later CERN, where particle creation and annihilation demonstrated mass-energy equivalence directly.
The 2022 CODATA recommended values provide the precise conversion factor: 1 eV/c² = 1.782661921 × 10⁻³⁶ kg, derived from fundamental constants including the elementary charge (e) and speed of light (c). This level of precision reflects advances in metrology and the quantum SI system adopted in 2019.
Frequently Asked Questions
What does eV/c² represent?
eV/c² represents mass expressed in energy units divided by the speed of light squared. It directly reflects Einstein’s E = mc² relationship, where 1 eV/c² equals the mass of a particle whose rest energy is 1 electronvolt. This unit is standard in particle physics because it naturally connects to the energies measured in accelerators and detectors.
Why is the conversion factor so small?
The conversion factor (1.783 × 10⁻³⁶ kg per eV/c²) is extremely small because the electronvolt is a tiny energy unit compared to the joule, and when divided by c² (approximately 9 × 10¹⁶ m²/s²), the resulting mass is minuscule. This reflects the quantum scale of subatomic particles—even an electron weighs only about 10⁻³⁰ kg.
Can I convert directly between MeV/c² and kg?
Yes, you can multiply MeV/c² by 1.783 × 10⁻³⁰ to get kilograms directly, since 1 MeV = 10⁶ eV. Similarly, 1 GeV/c² = 1.783 × 10⁻²⁷ kg. However, understanding the base conversion helps avoid errors when working with different energy scales.
How accurate is this conversion?
The conversion factor comes from the 2022 CODATA recommended values and is accurate to at least 10 significant figures. For most physics applications, using 1.783 × 10⁻³⁶ kg per eV/c² provides sufficient precision. The full value (1.782661921… × 10⁻³⁶) offers even greater accuracy when needed.
Why do particle physicists prefer eV/c² over kg?
eV/c² aligns with how particles are studied and created in accelerators, where energies are directly measured in electronvolts. It also makes comparing particle masses intuitive—a 1 GeV/c² particle has roughly 1000 times the mass of a 1 MeV/c² particle. Converting everything to kilograms would require constantly working with powers of 10⁻²⁷ or smaller.
What’s the relationship to atomic mass units (u)?
The atomic mass unit (u) equals 931.494 MeV/c² or 1.661 × 10⁻²⁷ kg. This connection allows conversion between nuclear physics (where masses are often in u) and particle physics (where eV/c² dominates). One proton mass is approximately 1.007 u or 938.3 MeV/c².
References
- National Institute of Standards and Technology (NIST). (2022). CODATA Recommended Values of the Fundamental Physical Constants: 2022. Journal of Physical and Chemical Reference Data. Retrieved from https://physics.nist.gov/cuu/Constants/
- Mohr, P. J., Newell, D. B., & Taylor, B. N. (2016). CODATA recommended values of the fundamental physical constants: 2014. Reviews of Modern Physics, 88(3), 035009.
- Einstein, A. (1905). Ist die Trägheit eines Körpers von seinem Energieinhalt abhängig? Annalen der Physik, 323(13), 639-641.
- Particle Data Group. (2022). Review of Particle Physics. Progress of Theoretical and Experimental Physics, 2022(8), 083C01.
- Griffiths, D. (2008). Introduction to Elementary Particles (2nd ed.). Wiley-VCH.