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Picometre
Picometre
Picometre
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Picometre
A simplified representation of a helium atom, having an estimated (calculated) diameter of 62 picometres[1]
General information
Unit systemSI
Unit oflength
Symbolpm
Conversions
1 pm in ...... is equal to ...
   SI base units   1×10−12 m
   Natural units   6.1877×1022 ℓP
   1.8897×10−2 a0
   imperial/US units   3.9370×10−11 in
Look up picometre in Wiktionary, the free dictionary.

The picometre (international spelling as used by the International Bureau of Weights and Measures; SI symbol: pm) or picometer (American spelling) is a unit of length in the International System of Units (SI), equal to 1×10−12 m, or one trillionth (⁠1/1000000000000⁠) of a metre, which is the SI base unit of length.

The picometre is one thousand femtometres, one thousandth of a nanometre (⁠1/1000⁠ nm), one millionth of a micrometre (also known as a micron), one billionth of a millimetre, and one trillionth of a metre.[2] The symbol μμ was once used for it.[3] It is also one hundredth of an ångström, an internationally known (but non-SI) unit of length.

Use

[edit]

The picometre's length is of an order so small that its application is almost entirely confined to particle physics, quantum physics, chemistry, and acoustics. Atoms are between 62 and 520 pm in diameter, and the typical length of a carbon–carbon single bond is 154 pm. Smaller units still may be used to describe smaller particles (some of which are the components of atoms themselves), such as hadrons and the upper limits of possible size for fermion point particles.

The Laser Interferometer Space Antenna (LISA) probe is planned for launch in 2034 to directly detect gravitational waves and will measure relative displacements with a resolution of 20 picometres over a distance of 2.5 gigametres, yielding a strain sensitivity of better than 1 part in 1020.

References

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Picometre

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The picometre (international spelling; also spelled picometer in ), abbreviated as pm, is a in the (SI) equal to 10−1210^{-12} s, or one trillionth (short scale) of a . This prefix "pico-", derived from the Spanish word pico meaning "a little bit," was formally adopted by the 11th General Conference on Weights and Measures (CGPM) in as part of the SI prefix system to denote factors of 10−1210^{-12}. The unit is particularly suited for expressing extremely small distances, such as those encountered in atomic and subatomic scales. In scientific applications, the picometre is predominantly used in fields like chemistry, physics, and materials science to quantify interatomic distances, bond lengths, and atomic radii. For instance, the bond length of a hydrogen molecule (H-H) is approximately 74 pm, while a typical carbon-carbon single bond measures about 154 pm, and double bonds are shorter at around 134 pm. These measurements are critical for understanding molecular structures, as seen in advanced techniques like picometre-resolution nuclear magnetic resonance (NMR) spectroscopy, which reveals coordination sphere details in metal-ligand complexes with precision down to 1 pm. The picometre's scale aligns closely with fundamental physical phenomena, including electron cloud extents and lattice vibrations in solids, where displacements as small as a few picometres can drive properties like in materials. Though less common in everyday contexts due to its minuteness—equivalent to about 0.01 angstroms (1 = 100 pm)—it remains indispensable for precise modeling in and research.

Definition

Etymology

The term "picometre" combines the SI prefix "pico-" with the base unit "metre," reflecting a linguistic fusion designed to denote extremely small lengths in scientific measurement. The prefix "pico-" derives from Romance languages, such as the Italian word piccolo meaning "small" or the Spanish word pico, meaning "a small quantity" or "tiny bit," which originally referred to a "beak" or "peak," evoking the idea of something pointed and minuscule. This etymological choice aligns with the metric system's tradition of drawing from Romance languages for prefixes indicating small scales, emphasizing conceptual smallness over literal translation. In the broader historical context of metric prefix etymologies, "pico-" emerged during the mid-20th century as scientists sought standardized terms for sub-microscopic magnitudes, building on earlier Greek and Latin roots for larger or moderately small units. The prefix was proposed in a 1940 draft by the International Federation of National Standardizing Associations and gained recognition through international chemistry and physics bodies, entering the scientific lexicon around 1948 before formal adoption in the SI system in 1960. This timeline highlights how "pico-" was selected for its phonetic brevity and intuitive connotation of tininess, facilitating its integration into for emerging fields like . The "" component traces its roots to the métron, meaning "measure" or "rule," a term that entered scientific usage via French mètre during the development of the in the late . When paired with "pico-," it specifically adapts this foundational to express scales a times smaller, underscoring the prefix's role in extending the metric system's linguistic framework to nanoscale and beyond.

Formal Definition and Value

The picometre (symbol: pm) is a unit of length in the (SI) that is equal to one trillionth of a , or exactly 10−1210^{-12} metres. This value was formally established with the adoption of the "pico-" prefix by the 11th General Conference on Weights and Measures (CGPM) in 1960.

History

Introduction of the Pico Prefix

The pico prefix, meaning "small" from Italian piccolo, was newly introduced in 1960 as part of the initial SI prefix set to denote factors of 10−1210^{-12}. It filled the need for expressing trillionths in scientific measurements, particularly in physics and chemistry, where smaller scales were increasingly studied.

Standardization in the SI System

The prefix "pico," denoting a factor of 10^{-12}, was officially adopted as part of the initial set of SI prefixes by the 11th General Conference on Weights and Measures (CGPM) in 1960 through Resolution 12, which established the (SI) and included prefixes ranging from hecto to pico to ensure consistent decimal scaling for SI units. Subsequent editions of the SI Brochure, first published by the International Bureau of Weights and Measures (BIPM) in 1970 and revised in 1975, reaffirmed the inclusion of the pico prefix without any modifications to its definition or value, maintaining its role in forming decimal submultiples of coherent SI units such as the . The 2019 revision of the SI, adopted by the 26th CGPM in 2018 and effective from 20 May , redefined several base units—including the in terms of the —but left the SI prefixes, including pico, unaltered, thereby preserving the as exactly 10^{-12} while enhancing the system's foundation on fixed constants. The International Committee for Weights and Measures (CIPM), established to oversee SI implementation, has consistently promoted global uniformity in the use of prefixes like pico through recommendations and consultations with international bodies, ensuring their consistent application across scientific and technical domains worldwide.

Scale and Comparisons

Illustrating the Magnitude

The picometre, equal to 10−1210^{-12} metres, represents an extraordinarily small length scale that defies everyday intuition. For context, the diameters of atoms typically range from about 60 to 500 picometres, with many around 100 to 200 picometres, meaning a single picometre spans a small of an atom's width. Similarly, the average diameter of a human measures around 70 micrometres, or 70 million picometres, so one picometre equates to roughly one-seventieth of a millionth the thickness of a . To aid visualization, consider a standard stick—the distance of a large step—divided into one equal segments; each segment would measure exactly one picometre. This subdivision highlights the picometre's minuteness, as it requires stacking a such units to span just one . At the picometre scale, classical intuitions break down, giving way to quantum phenomena where particles exhibit wave-like behaviour and probabilistic distributions dominate. Structures and processes at this level remain invisible to conventional microscopes, which are limited by the of visible to a resolution of about 200 nanometres—over 200,000 times larger than a picometre. Measurements at the picometre scale became feasible in the through advancements like diffraction, pioneered in 1912 by and the Braggs, which allowed determination of atomic spacings down to tens of picometres in crystal lattices. Electron microscopy, developed in the 1930s and refined thereafter, further enabled direct imaging approaching picometre resolution in the early , with advancements such as those reported in 2008 achieving resolutions down to a few picometres, overcoming the wavelength limitations of light-based techniques.

Relation to Other Length Units

The picometre (pm) is defined as exactly 10−1210^{-12} metres in the (SI), providing a precise scale for subatomic measurements. Within the SI , it relates to other units as follows: 1 pm = 10−310^{-3} nanometres (nm), 1 pm = 10−610^{-6} micrometres (μ\mum), and 1 pm = 10310^{3} femtometres (fm). These conversions stem directly from the decimal-based hierarchy of SI prefixes, where nano- denotes 10−910^{-9} m, micro- denotes 10−610^{-6} m, and femto- denotes 10−1510^{-15} m. In relation to non-SI units, 1 pm = 0.01 ångströms (Å), with the ångström defined as exactly 10−1010^{-10} m. The ångström unit, named after Anders Jonas Ångström, has been historically significant in crystallography for measuring atomic spacings and diffraction patterns, though it is now largely superseded by SI units in modern standards. For broader contextual scale, 1 pm = 10−1510^{-15} kilometres (km), underscoring its utility in domains far smaller than macroscopic lengths like planetary or terrestrial distances. A general conversion formula between picometres and metres is given by: length in pm = (length in ) ×1012\times 10^{12}. For example, a 1 object corresponds to 101210^{12} pm, illustrating the vast multiplier needed to express everyday lengths at this atomic resolution.

Uses

Atomic and Molecular Scales

In atomic and molecular scales, the picometre is used to quantify distances such as bond lengths, atomic radii, and intermolecular interactions. Typical covalent bond lengths range from about 100 pm to 200 pm; for example, a carbon-carbon measures approximately 154 pm, while a carbon-hydrogen bond is around 109 pm. Atomic radii for main-group elements generally fall between 50 pm and 200 pm, reflecting the size of electron clouds. Van der Waals distances between non-bonded atoms are larger, typically 300 pm to 400 pm, based on twice the van der Waals radii (e.g., 170 pm for carbon). The spatial extent of electron distributions in atoms—governed by quantum mechanical wavefunctions—reaches scales around 100 pm. In the , the provides a baseline with the most probable electron position () at 52.9 pm, but full probabilistic descriptions from Schrödinger's show the 1s orbital's root-mean-square radius extending to about 1.7 times this value, or roughly 90 pm, with tails decaying exponentially. For multi-electron atoms, outer electron clouds can span several hundred picometres, though remain more localized near the nucleus at sub-picometre distances. These extents illustrate the picometre's utility in describing atomic structures.

Subatomic and Nuclear Physics

In subatomic and , the picometre serves as a unit to quantify extremely small scales associated with nuclear structures and particle interactions. The radius of an is approximated by the semi-empirical formula R=r0A1/3R = r_0 A^{1/3}, where AA is the (total number of protons and neutrons) and r0r_0 is a constant approximately equal to 1.2 fm (or 1.2×10−31.2 \times 10^{-3} pm). This relation arises from the near-constant density of and predicts nuclear sizes on the order of femtometres, or 10−310^{-3} pm. For the proton (A=1A = 1), the formula yields R≈1.2R \approx 1.2 fm (1.2×10−31.2 \times 10^{-3} pm), though precise measurements of the proton charge radius from and muonic give a value of 0.84075(64)0.84075(64) fm, or about 8.41×10−48.41 \times 10^{-4} pm. For heavier nuclei, such as (A=238A = 238), the radius extends to roughly 7.4 fm (7.4×10−37.4 \times 10^{-3} pm), illustrating how the picometre frames the growth of nuclear dimensions with increasing count. Quarks and gluons, the fundamental constituents of protons and neutrons, do not exist in isolation due to in (QCD). This phenomenon confines these particles within on characteristic length scales of approximately 1 fm, equivalent to 10−310^{-3} pm, as determined by the QCD ΛQCD≈200\Lambda_{\rm QCD} \approx 200 MeV via the relation ℓ∼ℏc/ΛQCD\ell \sim \hbar c / \Lambda_{\rm QCD}. In simulations, this confinement manifests as a linear potential between rising with separation up to about 1 fm, beyond which formation dominates, preventing free observation. These picometre-scaled distances underscore the non-perturbative nature of strong interactions at low energies, where gluonic fields bind into color-neutral composites like mesons and baryons. Experimental probes of these subatomic structures rely on high-precision measurements achieving picometre-scale resolution through experiments. At CERN's (LHC), of protons at energies up to 13 TeV resolves internal quark-gluon dynamics on length scales down to 10−310^{-3} pm (femtometres), revealing parton distribution functions and confinement effects via transfers corresponding to probes. Similarly, electron-proton at facilities like Jefferson Lab measures form factors that map nuclear charge distributions with uncertainties below 0.01 fm (10−510^{-5} pm), confirming the A1/3A^{1/3} dependence and proton radius values. Such techniques, grounded in , use picometre units to contextualize the minuscule geometries inaccessible to direct imaging.
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