Orders of magnitude (time)

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An "order of magnitude" is a loose description of the relationship between two amounts. 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.

Seconds

Orders of magnitude (Time)
Factor (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) 5.4×10−20 ys = 5.4×10−44 s: One Planck time tP = \sqrt{\hbar G/c^5}5.4×10−44 s2 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 ys3 Yoctosecond, (yocto- + second), is one septillionth of a second 0.3 ys: mean life of the W and Z bosons.45a
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 bonding6
1 zs, 10 zs, 100 zs
10−18 1 attosecond as One quintillionth of one second 12 attoseconds: shortest measured period of time.7 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) 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)
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 rest8
4–8 ms: typical seek time for a computer hard disk
100–400 ms (=0.1–0.4 s): Blink of an eye9
18–300 ms (=0.02–0.3 s): Human reflex response to visual stimuli
1 ms, 10 ms, 100 ms
100 1 second s 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.10

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)11
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)

1012 s, 1013 s, 1014 s
1015 1 petasecond
(32 million years)
Ps One quadrillion seconds 7.1–7.9 Ps: 1 galactic year (225-250 million years)12

143 Ps: the age of the Earth131415
144 Ps: the approximate age of the Solar system16 and the Sun.17
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.

9.8 Zs: the lifetime of Brahma in Hindu mythology

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

See also

Years

Orders of magnitude (time)
Factor (a) Multiple Common units Orders of magnitude
10−50 Planck time, the shortest physically meaningful interval of time ≈ 1.71×10−50 a 10−50 a
10−24 1 yoctoannum 1 ya and less, 10 ya, 100 ya
10−21 1 zeptoannum 1 za, 10 za, 100 za
10−18 1 attoannum 1 aa, 10 aa, 100 aa
10−15 1 femtoannum 1 fa, 10 fa, 100 fa
10−12 1 picoannum 1 pa, 10 pa, 100 pa
10−9 1 nanoannum 1 second = 3.17 × 10−8 a ≈ 10-7.50 a 1 na, 10 na, 100 na
10−6 1 microannum 1 minute = 1.90 × 10−6 a
1 hour = 1.40 × 10−4 a
1 ua, 10 ua, 100 ua
10−3 1 milliannum 1 day = 2.73 × 10−3 a
1 week = 1.91 × 10−2 a
1 ma, 10 ma, 100 ma
100 1 annum 1 average year = 1 annum (= 365.24219 SI days)
1 decade = 10 a
1 century = 100 a
1 a, 10 a, 100 a
103 1 kiloannum millennium = 1000 a 103 a, 104 a, 105 a
106 1 megaannum epoch = 1,000,000 a 106 a, 107 a, 108 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
109 a, 1010 a, 1011 a
1012 1 teraannum 1012 a, 1013 a, 1014 a
1015 1 petaannum 1015 a, 1016 a, 1017 a
1018 1 exaannum 19 exaannum, the estimated half-life of the "stable" 20983Bi radioactive isotope 1018 a, 1019 a, 1020 a
1021 1 zettaannum 1021 a, 1022 a, 1023 a
1024 1 yottaannum 1024 a, 1025 a, 1026 and more

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 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

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)
  2. ^ "CODATA Value: Planck time". The NIST Reference on Constants, Units, and Uncertainty. NIST. Retrieved October 1, 2011. 
  3. ^ 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
  4. ^ C. Amsler et al. (2009): Particle listings – W boson
  5. ^ C. Amsler et al. (2009): Particle listings – Z boson
  6. ^ esciencenews (2010)
  7. ^ "12 attoseconds is the world record for shortest controllable time". 
  8. ^ http://www.noteaccess.com/APPROACHES/ArtEd/ChildDev/1cNeurons.htm
  9. ^ Eric H. Chudler. "Brain Facts and Figures: Sensory Apparatus: Vision". Retrieved October 10, 2011. 
  10. ^ http://tycho.usno.navy.mil/leapsec.html
  11. ^ CIA - The World Factbook -- Rank Order - Life expectancy at birth
  12. ^ Leong, Stacy (2002). "Period of the Sun's Orbit around the Galaxy (Cosmic Year)". The Physics Factbook. 
  13. ^ "Age of the Earth". U.S. Geological Survey. 1997. Retrieved January 10, 2006. 
  14. ^ Dalrymple, G. Brent (2001). "The age of the Earth in the twentieth century: a problem (mostly) solved". Special Publications, Geological Society of London 190 (1): 205–221. Bibcode:2001GSLSP.190..205D. doi:10.1144/GSL.SP.2001.190.01.14. 
  15. ^ Manhesa, Gérard; Allègrea, Claude J.; Dupréa, Bernard; and Hamelin, Bruno (1980). "Lead isotope study of basic-ultrabasic layered complexes: Speculations about the age of the earth and primitive mantle characteristics". Earth and Planetary Science Letters 47 (3): 370–382. Bibcode:1980E&PSL..47..370M. doi:10.1016/0012-821X(80)90024-2. 
  16. ^ 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.
  17. ^ Bonanno, A.; Schlattl, H.; Paternò, L. (2008). "The age of the Sun and the relativistic corrections in the EOS". Astronomy and Astrophysics 390 (3): 1115–1118. arXiv:astro-ph/0204331. Bibcode:2002A&A...390.1115B. doi:10.1051/0004-6361:20020749. 

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