Time (Orders of magnitude)

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In the context of time, an order of magnitude is a description of the quantity of a time in respect to comparison between differing magnitudes. In common usage, the scale is usually the base10 or base−10 exponent being applied to an amount, making the order of magnitude 10 times greater or smaller.[1] As the differences are measured in factors of 10, a logarithmic scale is applied. In terms of time, the relationship between the smallest limit of time, the Planck time, and the next order of magnitude larger is 10.

Low order of magnitude - measures by the unit second (s)

Unit (s) Multiple Symbol Definition Comparative examples & common units Orders of magnitude
10−44 1 Planck time tP The time required to travel one Planck length at the speed of light (c) 5.4 × 10-39 tP The time for a black hole the mass of the Earth to decay via Hawking radiation. [2]
5.4×10−20 ys = 5.4×10−44 s: One Planck time tP = \sqrt{\hbar G/c^5}5.4×10−44 s[3] is the briefest physically meaningful span of time. It is the unit of time in the natural units system known as Planck units.
10−20 ys, 10−19 ys (10−44 s, 10−43 s)
10−24 1 yoctosecond ys[4] Yoctosecond, (yocto- + second), is one septillionth of a second 0.3 ys: mean life of the W and Z bosons.[5][6][lower-alpha 1]
0.5 ys: time for top quark decay, according to the Standard Model.
1 ys: time taken for a quark to emit a gluon.
23 ys: half-life of 7H.
1 ys and less, 10 ys, 100 ys
10−21 1 zeptosecond zs Zeptosecond, (zepto- + second), is one sextillionth of one second 7 zs: half-life of helium-9's outer neutron in the second nuclear halo.
17 zs: approximate period of electromagnetic radiation at the boundary between gamma rays and X-rays.
300 zs: approximate typical cycle time of X-rays, on the boundary between hard and soft X-rays.
500 zs: current resolution of tools used to measure speed of chemical bonding[7]
1 zs, 10 zs, 100 zs
10−18 1 attosecond as One quintillionth of one second 12 attoseconds: shortest measured period of time.[8] 1 as, 10 as, 100 as
10−15 1 femtosecond fs One quadrillionth of one second 1 fs: Cycle time for 390 nanometre light; transition from visible light to ultraviolet; light travels 0.3 micrometers (µm).
140 fs: Electrons have localized onto individual bromine atoms 6Å apart after laser dissociation of Br2.[9]
1 fs, 10 fs, 100 fs
10−12 1 picosecond ps One trillionth of one second 1 ps: half-life of a bottom quark; light travels 0.3 millimeters (mm)
1 ps: lifetime of a transition state
4 ps: Time to execute one machine cycle by an IBM Silicon-Germanium transistor
1 ps, 10 ps, 100 ps
10−9 1 nanosecond ns One billionth of one second 1 ns: Time to execute one machine cycle by a 1 GHz microprocessor
1 ns: Light travels 30 centimetres (12 in)
1 ns, 10 ns, 100 ns
10−6 1 microsecond µs One millionth of one second 1 µs: Time to execute one machine cycle by an Intel 80186 microprocessor
4–16 µs: Time to execute one machine cycle by a 1960s minicomputer
1 µs, 10 µs, 100 µs
10−3 1 millisecond ms One thousandth of one second 1 ms: time for a neuron in human brain to fire one impulse and return to rest[10]
4–8 ms: typical seek time for a computer hard disk
100–400 ms (=0.1–0.4 s): Blink of an eye[11]
18–300 ms (=0.02–0.3 s): Human reflex response to visual stimuli
1 ms, 10 ms, 100 ms
100 1 second s The duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom. 1 s: 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom.[12]

60 s: 1 minute

1 s, 10 s, 100 s
103 1 kilosecond
(16.7 minutes)
ks One thousand seconds 3.6 ks: 3600 s or 1 hour
86.4 ks: 86 400 s or 1 day
604.8 ks: 1 week
103 s, 104 s, 105 s
106 1 megasecond
(11.6 days)
Ms One million seconds

2.6 Ms: approximately 1 month
31.6 Ms: approximately 1 year ≈ 107.50 s

106 s, 107 s, 108 s
109 1 gigasecond
(32 years)
Gs One billion seconds

2.1 Gs: average human life expectancy at birth (2011 estimate)[13]
3.16 Gs: approximately 1 century
31.6 Gs: approximately 1 millennium

109 s, 1010 s, 1011 s
1012 1 terasecond
(32 000 years)
Ts One trillion seconds

6 Ts: Time since the appearance of Homo sapiens (approximately)
80 Ts: Time it takes for light to travel from the Andromeda Galaxy to the Milky Way.[14]
160–220 Ts: Time since the divergence of the human and chimpanzee lineages.[15]

1012 s, 1013 s, 1014 s
1015 1 petasecond
(32 million years)
Ps One quadrillion seconds 2.1 Ps: (66 million years) Time elapsed since the Cretaceous–Paleogene extinction event, during which all non-avian dinosaurs became extinct. [16]

7.1–7.9 Ps: 1 galactic year (225-250 million years)[17]
143 Ps: the age of the Earth[18][19][20]
144 Ps: the approximate age of the Solar system[21] and the Sun.[22]
430 Ps: the approximate age of the Universe
440 Ps: the half-life of thorium 232

1015 s, 1016 s, 1017 s
1018 1 exasecond
(32 billion years)
Es One quintillion seconds 312 Es: Estimated lifespan of a 0.1 solar mass red dwarf star. 1018 s, 1019 s, 1020 s
1021 1 zettasecond
(32 trillion years)
Zs One sextillion seconds 3 Zs: Estimated duration of Stelliferous Era. 1021 s, 1022 s, 1023 s
1024 1 yottasecond
(32 quadrillion years)
Ys One septillion seconds 1.6416 Ys: Estimated half-life of the meta-stable 20983Bi radioactive isotope.

6.616×1050 Ys: Time required for a 1 solar mass black hole to evaporate completely due to Hawking radiation, if nothing more falls in.

1024 s, 1025 s, 1026 s and more

High order of magnitude - measures by the unit year (a)

Unit (a) Multiple Common units
10−50 Planck time, the shortest physically meaningful interval of time ≈ 1.71×10−50 a
10−24 1 yoctoannum
10−21 1 zeptoannum
10−18 1 attoannum
10−15 1 femtoannum
10−12 1 picoannum
10−9 1 nanoannum 1 second = 3.17 × 10−8 a ≈ 10−7.50 a
10−6 1 microannum 1 minute = 1.90 × 10−6 a
1 hour = 1.40 × 10−4 a
10−3 1 milliannum 1 day = 2.73 × 10−3 a
1 week = 1.91 × 10−2 a
100 1 annum 1 average year = 1 annum (= 365.24219 SI days)
1 decade = 10 a
1 century = 100 a
103 1 kiloannum millennium = 1000 a
106 1 megaannum epoch = 1,000,000 a
109 1 gigaannum aeon = 1,000,000,000 a
13.8 Ga = 1.38×1010 a ≈ 13.8 billion years, the approximate age of the Universe
1012 1 teraannum
1015 1 petaannum
1018 1 exaannum 19 exaannum, the estimated half-life of the "stable" 20983Bi radioactive isotope
1021 1 zettaannum
1024 1 yottaannum

The pages linked in the right-hand column contain lists of times that are of the same order of magnitude (power of ten). Rows in the table represent increasing powers of a thousand (3 orders of magnitude).

Conversion from year to second is year × 31 557 600 (approximately \pi * 10^7) using the Julian year. Conversion from \log_{10} \mbox{ year} to \log_{10} \mbox{ second} is approximately \log_{10} \mbox{ year} + 7.50. Example conversion; 1 \mbox{ year} =10^0 \mbox{ year} = 10^{0+7.50} \mbox{ seconds } = 10^{0.50 + 7} s = 3.16 * 10^7 s.

See also

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Footnotes

Notes
  1. PDG reports the resonance width (Γ). Here the conversion τ = ​ħΓ is given instead.
References
  1. Brians, Paus. "Orders of Magnitude" (8/4/2013)
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  4. The American Heritage Dictionary of the English Language: Fourth Edition. 2000. Available at: http://www.bartleby.com/61/21/Y0022100.html. Accessed December 19, 2007. note: abbr. ys or ysec
  5. C. Amsler et al. (2009): Particle listings – W boson
  6. C. Amsler et al. (2009): Particle listings – Z boson
  7. esciencenews (2010)
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  10. http://www.noteaccess.com/APPROACHES/ArtEd/ChildDev/1cNeurons.htm
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  12. http://tycho.usno.navy.mil/leapsec.html
  13. CIA - The World Factbook -- Rank Order - Life expectancy at birth
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  21. Bouvier, Audrey and Meenakshi Wadhwa, "The age of the solar system redefined by the oldest Pb-Pb age of a meteoritic inclusion". Nature Geoscience, Nature Publishing Group, a division of Macmillan Publishers Limited. Published online August 22, 2010, retrieved August 26, 2010, doi:10.1038/NGEO941.
  22. Lua error in package.lua at line 80: module 'strict' not found.

External links