# Femtosecond

A femtosecond is a unit of time in the International System of Units (SI) equal to 10-15 or 11 000 000 000 000 000 of a second; that is, one quadrillionth, or one millionth of one billionth, of a second.[1] For context, a femtosecond is to a second as a second is to about 31.71 million years; a ray of light travels approximately 0.3 μm (micrometers) in 1 femtosecond, a distance comparable to the diameter of a virus.[2]

The word femtosecond is formed by the SI prefix femto and the SI unit second. Its symbol is fs.[3]

A femtosecond is equal to 1000 attoseconds, or 1/1000 picosecond. Because the next higher SI unit is 1000 times larger, times of 10−14 and 10−13 seconds are typically expressed as tens or hundreds of femtoseconds.

• Typical time steps for molecular dynamics simulations are on the order of 1 fs.[4]
• The periods of the waves of visible light have a duration of about 2 femtoseconds. ${\displaystyle {\lambda \over {c}}={600\times 10^{-9}~{\rm {m}} \over 3\times 10^{8}~{\rm {m}}~{\rm {s}}^{-1}}=2.0\times 10^{-15}~{\rm {s}}}$ The precise duration depends on the energy of the photons, which determines their color. (See wave–particle duality.) This time can be calculated by dividing the wavelength of the light by the speed of light (approximately 3×108 m/s) to determine the time required for light to travel that distance.[5]
The colors of the visible light spectrum[6]
Color Wavelength
interval
Cycle time
interval
Red ~ 700–635 nm ~ 2.3–2.1 fs
Orange ~ 635–590 nm ~ 2.1-2.0 fs
Yellow ~ 590–560 nm ~ 2.0-1.9 fs
Green ~ 560–520 nm ~ 1.9-1.7 fs
Cyan ~ 520–490 nm ~ 1.7-1.6 fs
Blue ~ 490–450 nm ~ 1.6-1.5 fs
Violet ~ 450–400 nm ~ 1.5-1.3 fs

## Examples

• 46 fs – the swiftest chemical reaction known (radiolysis of water leads to the formation of a H2O+ ion, which rapidly reacts to become hydronium (H3O+) and a short lived hydrogen monoxide molecule (OH))[7]
• 200 fs – the average chemical reaction, such as the reaction of pigments in an eye to light[5]
• 300 fs – the duration of a vibration of the atoms in an iodine molecule[8]

## References

1. ^ "Femtosecond: Merriam Webster definition". Merriam Webster Online Dictionary.
2. ^ Compared with overview in: Fisher, Bruce; Harvey, Richard P.; Champe, Pamela C. (2007). Lippincott's Illustrated Reviews: Microbiology (Lippincott's Illustrated Reviews Series). Hagerstown, MD: Lippincott Williams & Wilkins. ISBN 978-0-7817-8215-9. Page 3
3. ^
4. ^ "Femtosecond: use in molecular dynamics simulation". LAMMPS Molecular Simulator.
5. ^ a b Andrew M. Weiner (2009). Ultrafast Optics. Wiley. ISBN 978-0-471-41539-8.
6. ^ Craig F. Bohren (2006). Fundamentals of Atmospheric Radiation: An Introduction with 400 Problems. Wiley-VCH. p. 214. Bibcode:2006fari.book.....B. ISBN 978-3-527-40503-9.
7. ^ Loh, Z.-H.; Doumy, G.; Arnold, C.; Kjellsson, L.; Southworth, S. H.; Al Haddad, A.; Kumagai, Y.; Tu, M.-F.; Ho, P. J.; March, A. M.; Schaller, R. D.; Bin Mohd Yusof, M. S.; Debnath, T.; Simon, M.; Welsch, R. (2020-01-10). "Observation of the fastest chemical processes in the radiolysis of water". Science. 367 (6474): 179–182. doi:10.1126/science.aaz4740. ISSN 0036-8075.
8. ^ Abbi, S. C. (2001). Nonlinear Optics and Laser Spectroscopy. United States of America: Alpha Science Int'l Ltd. p. 361. ISBN 8173193541.