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[edit]

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 s[2] 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[3] Yoctosecond, (yocto- + second), is one septillionth of a second 0.3 ys: mean life of the W and Z bosons.[4][5][a]
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[6]
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 rest[8]
4–8 ms: typical seek time for a computer hard disk
100–400 ms (=0.1–0.4 s): Blink of an eye[9]
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 Earth[13][14][15]
144 Ps: the approximate age of the Solar system[16] 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[edit]

Years[edit]

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[edit]

Footnotes[edit]

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. 

External links[edit]