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122-551: Deuterium ( hydrogen-2 , symbol H or D , also known as heavy hydrogen ) is one of two stable isotopes of hydrogen ; the other is protium, or hydrogen-1, H. The deuterium nucleus ( deuteron ) contains one proton and one neutron , whereas the far more common H has no neutrons. Deuterium has a natural abundance in Earth's oceans of about one atom of deuterium in every 6,420 atoms of hydrogen. Thus, deuterium accounts for about 0.0156% by number (0.0312% by mass) of all hydrogen in

244-433: A health threat to humans. It is estimated that a 70 kg (154 lb) person might drink 4.8 litres (1.3 US gal) of heavy water without serious consequences. Small doses of heavy water (a few grams in humans, containing an amount of deuterium comparable to that normally present in the body) are routinely used as harmless metabolic tracers in humans and animals. The deuteron has spin +1 (" triplet state ") and

366-404: A "complete standstill" by passing it through a Bose–Einstein condensate of the element rubidium . The popular description of light being "stopped" in these experiments refers only to light being stored in the excited states of atoms, then re-emitted at an arbitrarily later time, as stimulated by a second laser pulse. During the time it had "stopped", it had ceased to be light. This type of behaviour

488-473: A deuterium nucleus (actually a highly excited state of it), a nucleus with two protons, and a nucleus with two neutrons. These states are not stable. The deuteron wavefunction must be antisymmetric if the isospin representation is used (since a proton and a neutron are not identical particles, the wavefunction need not be antisymmetric in general). Apart from their isospin, the two nucleons also have spin and spatial distributions of their wavefunction. The latter

610-505: A further 4–24 minutes for commands to travel from Earth to Mars. Receiving light and other signals from distant astronomical sources takes much longer. For example, it takes 13 billion (13 × 10 ) years for light to travel to Earth from the faraway galaxies viewed in the Hubble Ultra-Deep Field images. Those photographs, taken today, capture images of the galaxies as they appeared 13 billion years ago, when

732-544: A higher boiling point (23.64 vs. 20.27 K), a higher critical temperature (38.3 vs. 32.94 K) and a higher critical pressure (1.6496 vs. 1.2858 MPa). The physical properties of deuterium compounds can exhibit significant kinetic isotope effects and other physical and chemical property differences from the protium analogs. H 2 O, for example, is more viscous than normal H 2 O . There are differences in bond energy and length for compounds of heavy hydrogen isotopes compared to protium, which are larger than

854-464: A light year is nearly 10 trillion kilometres or nearly 6 trillion miles. Proxima Centauri , the closest star to Earth after the Sun, is around 4.2 light-years away. Radar systems measure the distance to a target by the time it takes a radio-wave pulse to return to the radar antenna after being reflected by the target: the distance to the target is half the round-trip transit time multiplied by

976-615: A material-dependent constant. The refractive index of air is approximately 1.0003. Denser media, such as water , glass , and diamond , have refractive indexes of around 1.3, 1.5 and 2.4, respectively, for visible light. In exotic materials like Bose–Einstein condensates near absolute zero, the effective speed of light may be only a few metres per second. However, this represents absorption and re-radiation delay between atoms, as do all slower-than- c speeds in material substances. As an extreme example of light "slowing" in matter, two independent teams of physicists claimed to bring light to

1098-413: A neutron and an "up" state (↑) being a proton. A pair of nucleons can either be in an antisymmetric state of isospin called singlet , or in a symmetric state called triplet . In terms of the "down" state and "up" state, the singlet is This is a nucleus with one proton and one neutron, i.e. a deuterium nucleus. The triplet is and thus consists of three types of nuclei, which are supposed to be symmetric:

1220-412: A process that uses hydrogen sulfide gas at high pressure. While India is self-sufficient in heavy water for its own use, India also exports reactor-grade heavy water. Formula: D 2 or 1 H 2 Data at about 18 K for H 2 ( triple point ): Compared to hydrogen in its natural composition on Earth, pure deuterium (H 2 ) has a higher melting point (18.72 K vs. 13.99 K),

1342-598: A ratio of as much as 23 atoms of deuterium per million hydrogen atoms in undisturbed gas clouds, which is only 15% below the WMAP estimated primordial ratio of about 27 atoms per million from the Big Bang. This has been interpreted to mean that less deuterium has been destroyed in star formation in the Milky Way galaxy than expected, or perhaps deuterium has been replenished by a large in-fall of primordial hydrogen from outside

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1464-584: A result, if something were travelling faster than  c relative to an inertial frame of reference, it would be travelling backwards in time relative to another frame, and causality would be violated. In such a frame of reference, an "effect" could be observed before its "cause". Such a violation of causality has never been recorded, and would lead to paradoxes such as the tachyonic antitelephone . There are situations in which it may seem that matter, energy, or information-carrying signal travels at speeds greater than  c , but they do not. For example, as

1586-449: A sample of water from an aquifer , and a sufficiently sensitive tool to measure the variation in the isotopic ratio of hydrogen in the sample, it is possible to infer the source, be it ocean water or precipitation seeping into the aquifer, and even to estimate the proportions from each source. Stable isotopologues of water are also used in partitioning water sources for plant transpiration and groundwater recharge . Another application

1708-416: A standard for the metre. As a dimensional physical constant , the numerical value of c is different for different unit systems. For example, in imperial units , the speed of light is approximately 186 282 miles per second, or roughly 1 foot per nanosecond. In branches of physics in which c appears often, such as in relativity, it is common to use systems of natural units of measurement or

1830-412: A time dilation factor of γ  = 2 occurs at a relative velocity of 86.6% of the speed of light ( v  = 0.866  c ). Similarly, a time dilation factor of γ  = 10 occurs at 99.5% the speed of light ( v  = 0.995  c ). The results of special relativity can be summarized by treating space and time as a unified structure known as spacetime (with  c relating

1952-459: A time interval of 1 ⁄ 299 792 458 of a second", fixing the value of the speed of light at 299 792 458  m/s by definition, as described below . Consequently, accurate measurements of the speed of light yield an accurate realization of the metre rather than an accurate value of c . Outer space is a convenient setting for measuring the speed of light because of its large scale and nearly perfect vacuum . Typically, one measures

2074-541: Is about 10.6% denser than normal water (so that ice made from it sinks in normal water). Heavy water is slightly toxic in eukaryotic animals, with 25% substitution of the body water causing cell division problems and sterility, and 50% substitution causing death by cytotoxic syndrome (bone marrow failure and gastrointestinal lining failure). Prokaryotic organisms, however, can survive and grow in pure heavy water, though they develop slowly. Despite this toxicity, consumption of heavy water under normal circumstances does not pose

2196-410: Is about three times that of Earth water. This figure is the highest yet measured in a comet. HHR's thus continue to be an active topic of research in both astronomy and climatology. Deuterium is often represented by the chemical symbol D. Since it is an isotope of hydrogen with mass number 2, it is also represented by H. IUPAC allows both D and H, though H is preferred. A distinct chemical symbol

2318-420: Is about three times that of Earth water. This has caused renewed interest in suggestions that Earth's water may be partly of asteroidal origin. Deuterium has also been observed to be concentrated over the mean solar abundance in other terrestrial planets, in particular Mars and Venus. Deuterium is produced for industrial, scientific and military purposes, by starting with ordinary water—a small fraction of which

2440-623: Is another one of the arguments in favor of the Big Bang over the Steady State theory of the Universe. The observed ratios of hydrogen to helium to deuterium in the universe are difficult to explain except with a Big Bang model. It is estimated that the abundances of deuterium have not evolved significantly since their production about 13.8 billion years ago. Measurements of Milky Way galactic deuterium from ultraviolet spectral analysis show

2562-413: Is antisymmetric under nucleons exchange due to isospin, and therefore must be symmetric under the double exchange of their spin and location. Therefore, it can be in either of the following two different states: In the first case the deuteron is a spin triplet, so that its total spin s is 1. It also has an even parity and therefore even orbital angular momentum l . The lower its orbital angular momentum,

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2684-417: Is barely bound at E B = 2.23 MeV , and none of the higher energy states are bound. The singlet deuteron is a virtual state, with a negative binding energy of ~60 keV . There is no such stable particle, but this virtual particle transiently exists during neutron–proton inelastic scattering, accounting for the unusually large neutron scattering cross-section of the proton. The deuterium nucleus

2806-442: Is called a deuteron . It has a mass of 2.013 553 212 544 (15) Da ‍ (just over 1.875 GeV/ c ). The charge radius of a deuteron is 2.127 78 (27) × 10 m . Like the proton radius , measurements using muonic deuterium produce a smaller result: 2.125 62 (78)  fm . Deuterium is one of only five stable nuclides with an odd number of protons and an odd number of neutrons. (H, Li , B , N , Ta ;

2928-424: Is described as a type of electromagnetic wave . The classical behaviour of the electromagnetic field is described by Maxwell's equations , which predict that the speed  c with which electromagnetic waves (such as light) propagate in vacuum is related to the distributed capacitance and inductance of vacuum, otherwise respectively known as the electric constant ε 0 and the magnetic constant μ 0 , by

3050-421: Is discussed in the propagation of light in a medium section below, many wave velocities can exceed  c . The phase velocity of X-rays through most glasses can routinely exceed c , but phase velocity does not determine the velocity at which waves convey information. If a laser beam is swept quickly across a distant object, the spot of light can move faster than  c , although the initial movement of

3172-427: Is frame-independent, because it is impossible to measure the one-way speed of light (for example, from a source to a distant detector) without some convention as to how clocks at the source and at the detector should be synchronized. By adopting Einstein synchronization for the clocks, the one-way speed of light becomes equal to the two-way speed of light by definition. The special theory of relativity explores

3294-511: Is from the distant past, allowing humans to study the history of the universe by viewing distant objects. When communicating with distant space probes , it can take minutes to hours for signals to travel. In computing , the speed of light fixes the ultimate minimum communication delay . The speed of light can be used in time of flight measurements to measure large distances to extremely high precision. Ole Rømer first demonstrated in 1676 that light does not travel instantaneously by studying

3416-459: Is generally microscopically true of all transparent media which "slow" the speed of light. In transparent materials, the refractive index generally is greater than 1, meaning that the phase velocity is less than c . In other materials, it is possible for the refractive index to become smaller than   1 for some frequencies; in some exotic materials it is even possible for the index of refraction to become negative. The requirement that causality

3538-505: Is important in determining how a light wave travels through a material or from one material to another. It is often represented in terms of a refractive index . The refractive index of a material is defined as the ratio of c to the phase velocity  v p in the material: larger indices of refraction indicate lower speeds. The refractive index of a material may depend on the light's frequency, intensity, polarization , or direction of propagation; in many cases, though, it can be treated as

3660-486: Is impossible for signals or energy to travel faster than  c . One argument for this follows from the counter-intuitive implication of special relativity known as the relativity of simultaneity . If the spatial distance between two events A and B is greater than the time interval between them multiplied by  c then there are frames of reference in which A precedes B, others in which B precedes A, and others in which they are simultaneous. As

3782-404: Is in paleotemperature measurement for paleoclimatology . For example, one technique is based on the variation in isotopic fractionation of oxygen by biological systems with temperature. Species of Foraminifera incorporate oxygen as calcium carbonate in their shells. The ratio of the oxygen isotopes oxygen-16 and oxygen-18 incorporated into the calcium carbonate varies with temperature and

Deuterium - Misplaced Pages Continue

3904-559: Is in part because the proportions of stable isotopes in these light and volatile elements is relatively easy to measure. However, recent advances in isotope ratio mass spectrometry (i.e. multiple-collector inductively coupled plasma mass spectrometry) now enable the measurement of isotope ratios in heavier stable elements, such as iron , copper , zinc , molybdenum , etc. The variations in oxygen and hydrogen isotope ratios have applications in hydrology since most samples lie between two extremes, ocean water and Arctic/Antarctic snow. Given

4026-402: Is in the s = 1 , l = 0 state. The same considerations lead to the possible states of an isospin triplet having s = 0 , l = even or s = 1 , l = odd . Thus, the state of lowest energy has s = 1 , l = 1 , higher than that of the isospin singlet. The analysis just given is in fact only approximate, both because isospin is not an exact symmetry, and more importantly because

4148-422: Is independent of the motion of the light source. He explored the consequences of that postulate by deriving the theory of relativity and, in doing so, showed that the parameter c had relevance outside of the context of light and electromagnetism. Massless particles and field perturbations, such as gravitational waves , also travel at speed c in vacuum. Such particles and waves travel at c regardless of

4270-500: Is known as the Lorentz factor and is given by γ = (1 − v / c ) , where v is the speed of the object. The difference of γ from   1 is negligible for speeds much slower than  c , such as most everyday speeds – in which case special relativity is closely approximated by Galilean relativity  – but it increases at relativistic speeds and diverges to infinity as v approaches c . For example,

4392-476: Is naturally occurring heavy water —and then separating out the heavy water by the Girdler sulfide process , distillation, or other methods. In theory, deuterium for heavy water could be created in a nuclear reactor, but separation from ordinary water is the cheapest bulk production process. The world's leading supplier of deuterium was Atomic Energy of Canada Limited until 1997, when the last heavy water plant

4514-491: Is not violated implies that the real and imaginary parts of the dielectric constant of any material, corresponding respectively to the index of refraction and to the attenuation coefficient , are linked by the Kramers–Kronig relations . In practical terms, this means that in a material with refractive index less than 1, the wave will be absorbed quickly. A pulse with different group and phase velocities (which occurs if

4636-559: Is observed, so information cannot be transmitted in this manner. Another quantum effect that predicts the occurrence of faster-than-light speeds is called the Hartman effect : under certain conditions the time needed for a virtual particle to tunnel through a barrier is constant, regardless of the thickness of the barrier. This could result in a virtual particle crossing a large gap faster than light. However, no information can be sent using this effect. So-called superluminal motion

4758-473: Is possible for a particle to travel through a medium faster than the phase velocity of light in that medium (but still slower than c ). When a charged particle does that in a dielectric material, the electromagnetic equivalent of a shock wave , known as Cherenkov radiation , is emitted. The speed of light is of relevance to telecommunications : the one-way and round-trip delay time are greater than zero. This applies from small to astronomical scales. On

4880-401: Is seen in certain astronomical objects, such as the relativistic jets of radio galaxies and quasars . However, these jets are not moving at speeds in excess of the speed of light: the apparent superluminal motion is a projection effect caused by objects moving near the speed of light and approaching Earth at a small angle to the line of sight: since the light which was emitted when the jet

5002-439: Is symmetric if the deuteron is symmetric under parity (i.e. has an "even" or "positive" parity), and antisymmetric if the deuteron is antisymmetric under parity (i.e. has an "odd" or "negative" parity). The parity is fully determined by the total orbital angular momentum of the two nucleons: if it is even then the parity is even (positive), and if it is odd then the parity is odd (negative). The deuteron, being an isospin singlet,

Deuterium - Misplaced Pages Continue

5124-453: Is the ratio found in the gas giant planets, such as Jupiter. The analysis of deuterium–protium ratios (HHR) in comets found results very similar to the mean ratio in Earth's oceans (156 atoms of deuterium per 10 hydrogen atoms). This reinforces theories that much of Earth's ocean water is of cometary origin. The HHR of comet 67P/Churyumov–Gerasimenko , as measured by the Rosetta space probe,

5246-429: Is thought to have played an important role in setting the number and ratios of the elements that were formed in the Big Bang . Combining thermodynamics and the changes brought about by cosmic expansion, one can calculate the fraction of protons and neutrons based on the temperature at the point that the universe cooled enough to allow formation of nuclei . This calculation indicates seven protons for every neutron at

5368-433: Is thought to represent close to the primordial Solar System ratio. This is about 17% of the terrestrial ratio of 156 deuterium atoms per million hydrogen atoms. Comets such as Comet Hale-Bopp and Halley's Comet have been measured to contain more deuterium (about 200 atoms per million hydrogens), ratios which are enriched with respect to the presumed protosolar nebula ratio, probably due to heating, and which are similar to

5490-490: Is thus a boson . The NMR frequency of deuterium is significantly different from normal hydrogen. Infrared spectroscopy also easily differentiates many deuterated compounds, due to the large difference in IR absorption frequency seen in the vibration of a chemical bond containing deuterium, versus light hydrogen. The two stable isotopes of hydrogen can also be distinguished by using mass spectrometry . The triplet deuteron nucleon

5612-491: Is used for convenience because of the isotope's common use in various scientific processes. Also, its large mass difference with protium (H) confers non-negligible chemical differences with H compounds. Deuterium has a mass of 2.014 102   Da , about twice the mean hydrogen atomic weight of 1.007 947  Da , or twice protium's mass of 1.007 825  Da . The isotope weight ratios within other elements are largely insignificant in this regard. In quantum mechanics ,

5734-559: The Deep Space Network determine distances to the Moon, planets and spacecraft, respectively, by measuring round-trip transit times. There are different ways to determine the value of c . One way is to measure the actual speed at which light waves propagate, which can be done in various astronomical and Earth-based setups. It is also possible to determine c from other physical laws where it appears, for example, by determining

5856-471: The Solar System (as confirmed by planetary probes), and in the spectra of stars , is also an important datum in cosmology . Gamma radiation from ordinary nuclear fusion dissociates deuterium into protons and neutrons, and there is no known natural process other than Big Bang nucleosynthesis that might have produced deuterium at anything close to its observed natural abundance. Deuterium is produced by

5978-417: The electromagnetic interaction relative to the strong nuclear interaction . The symmetry relating the proton and neutron is known as isospin and denoted I (or sometimes T ). Isospin is an SU(2) symmetry, like ordinary spin , so is completely analogous to it. The proton and neutron, each of which have iso spin-1/2 , form an isospin doublet (analogous to a spin doublet ), with a "down" state (↓) being

6100-400: The geometrized unit system where c = 1 . Using these units, c does not appear explicitly because multiplication or division by   1 does not affect the result. Its unit of light-second per second is still relevant, even if omitted. The speed at which light waves propagate in vacuum is independent both of the motion of the wave source and of the inertial frame of reference of

6222-459: The local speed of light is constant and equal to  c , but the speed of light can differ from  c when measured from a remote frame of reference, depending on how measurements are extrapolated to the region. It is generally assumed that fundamental constants such as  c have the same value throughout spacetime, meaning that they do not depend on location and do not vary with time. However, it has been suggested in various theories that

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6344-430: The printed circuit board refracts and slows down signals. Processors must therefore be placed close to each other, as well as memory chips, to minimize communication latencies, and care must be exercised when routing wires between them to ensure signal integrity . If clock frequencies continue to increase, the speed of light may eventually become a limiting factor for the internal design of single chips . Given that

6466-427: The quantum state of the deuterium is a superposition (a linear combination) of the s = 1 , l = 0 state and the s = 1 , l = 2 state, even though the first component is much bigger. Since the total angular momentum j is also a good quantum number (it is a constant in time), both components must have the same j , and therefore j = 1 . This is the total spin of the deuterium nucleus. To summarize,

6588-400: The quantum states of two particles that can be entangled . Until either of the particles is observed, they exist in a superposition of two quantum states. If the particles are separated and one particle's quantum state is observed, the other particle's quantum state is determined instantaneously. However, it is impossible to control which quantum state the first particle will take on when it

6710-427: The reduced mass of the deuterium is markedly higher than that of protium. In nuclear magnetic resonance spectroscopy , deuterium has a very different NMR frequency (e.g. 61 MHz when protium is at 400 MHz) and is much less sensitive. Deuterated solvents are usually used in protium NMR to prevent the solvent from overlapping with the signal, though deuterium NMR on its own right is also possible. Deuterium

6832-414: The speed of light may have changed over time . No conclusive evidence for such changes has been found, but they remain the subject of ongoing research. It is generally assumed that the two-way speed of light is isotropic , meaning that it has the same value regardless of the direction in which it is measured. Observations of the emissions from nuclear energy levels as a function of the orientation of

6954-524: The strong nuclear interaction between the two nucleons is related to angular momentum in spin–orbit interaction that mixes different s and l states. That is, s and l are not constant in time (they do not commute with the Hamiltonian ), and over time a state such as s = 1 , l = 0 may become a state of s = 1 , l = 2 . Parity is still constant in time, so these do not mix with odd l states (such as s = 0 , l = 1 ). Therefore,

7076-499: The Earth with speeds proportional to their distances. Beyond a boundary called the Hubble sphere , the rate at which their distance from Earth increases becomes greater than the speed of light. These recession rates, defined as the increase in proper distance per cosmological time , are not velocities in a relativistic sense. Faster-than-light cosmological recession speeds are only a coordinate artifact. In classical physics , light

7198-494: The H had been highly concentrated. The discovery of deuterium won Urey a Nobel Prize in 1934. Deuterium is destroyed in the interiors of stars faster than it is produced. Other natural processes are thought to produce only an insignificant amount of deuterium. Nearly all deuterium found in nature was produced in the Big Bang 13.8 billion years ago, as the basic or primordial ratio of H to H (≈26 atoms of deuterium per 10 hydrogen atoms) has its origin from that time. This

7320-436: The Universe became cool enough to form deuterium (at about a temperature equivalent to 100  keV ). At this point, there was a sudden burst of element formation (first deuterium, which immediately fused into helium). However, very soon thereafter, at twenty minutes after the Big Bang, the Universe became too cool for any further nuclear fusion or nucleosynthesis. At this point, the elemental abundances were nearly fixed, with

7442-434: The advantage which radio waves travelling at near to the speed of light through air have over comparatively slower fibre optic signals. Similarly, communications between the Earth and spacecraft are not instantaneous. There is a brief delay from the source to the receiver, which becomes more noticeable as distances increase. This delay was significant for communications between ground control and Apollo 8 when it became

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7564-413: The apparent motion of Jupiter 's moon Io . Progressively more accurate measurements of its speed came over the following centuries. In a paper published in 1865, James Clerk Maxwell proposed that light was an electromagnetic wave and, therefore, travelled at speed c . In 1905, Albert Einstein postulated that the speed of light c with respect to any inertial frame of reference is a constant and

7686-418: The appearance of certain high-speed astronomical objects , and particular quantum effects ). The expansion of the universe is understood to exceed the speed of light beyond a certain boundary . The speed at which light propagates through transparent materials , such as glass or air, is less than c ; similarly, the speed of electromagnetic waves in wire cables is slower than c . The ratio between c and

7808-440: The beginning of nucleogenesis , a ratio that would remain stable even after nucleogenesis was over. This fraction was in favor of protons initially, primarily because the lower mass of the proton favored their production. As the Universe expanded, it cooled. Free neutrons and protons are less stable than helium nuclei, and the protons and neutrons had a strong energetic reason to form helium-4 . However, forming helium-4 requires

7930-703: The broad diets of seabirds, and to identify the geographical areas where individuals spend the breeding and non-breeding season in seabirds and passerines. Numerous ecological studies have also used isotope analyses to understand migration, food-web structure, diet, and resource use, such as hydrogen isotopes to measure how much energy from stream-side trees supports fish growth in aquatic habitats. Determining diets of aquatic animals using stable isotopes has been particularly common, as direct observations are difficult. They also enable researchers to measure how human interactions with wildlife, such as fishing, may alter natural diets. In forensic science, research suggests that

8052-587: The consequences of this invariance of c with the assumption that the laws of physics are the same in all inertial frames of reference. One consequence is that c is the speed at which all massless particles and waves, including light, must travel in vacuum. Special relativity has many counterintuitive and experimentally verified implications. These include the equivalence of mass and energy ( E = mc ) , length contraction (moving objects shorten), and time dilation (moving clocks run more slowly). The factor  γ by which lengths contract and times dilate

8174-416: The deuterium nucleus is antisymmetric in terms of isospin, and has spin 1 and even (+1) parity. The relative angular momentum of its nucleons l is not well defined, and the deuteron is a superposition of mostly l = 0 with some l = 2 . In order to find theoretically the deuterium magnetic dipole moment μ , one uses the formula for a nuclear magnetic moment with g and g are g -factors of

8296-454: The distance between two objects in a frame of reference with respect to which both are moving (their closing speed ) may have a value in excess of  c . However, this does not represent the speed of any single object as measured in a single inertial frame. Certain quantum effects appear to be transmitted instantaneously and therefore faster than c , as in the EPR paradox . An example involves

8418-479: The emitting nuclei in a magnetic field (see Hughes–Drever experiment ), and of rotating optical resonators (see Resonator experiments ) have put stringent limits on the possible two-way anisotropy . According to special relativity, the energy of an object with rest mass m and speed v is given by γmc , where γ is the Lorentz factor defined above. When v is zero, γ is equal to one, giving rise to

8540-675: The energy levels of electrons in atoms depend on the reduced mass of the system of electron and nucleus. For a hydrogen atom , the role of reduced mass is most simply seen in the Bohr model of the atom, where the reduced mass appears in a simple calculation of the Rydberg constant and Rydberg equation, but the reduced mass also appears in the Schrödinger equation , and the Dirac equation for calculating atomic energy levels. The reduced mass of

8662-418: The equation In modern quantum physics , the electromagnetic field is described by the theory of quantum electrodynamics (QED). In this theory, light is described by the fundamental excitations (or quanta) of the electromagnetic field, called photons . In QED, photons are massless particles and thus, according to special relativity, they travel at the speed of light in vacuum. Extensions of QED in which

8784-512: The equatorial circumference of the Earth is about 40 075  km and that c is about 300 000  km/s , the theoretical shortest time for a piece of information to travel half the globe along the surface is about 67 milliseconds. When light is traveling in optical fibre (a transparent material ) the actual transit time is longer, in part because the speed of light is slower by about 35% in optical fibre, depending on its refractive index n . Straight lines are rare in global communications and

8906-495: The famous E = mc formula for mass–energy equivalence. The γ factor approaches infinity as v approaches  c , and it would take an infinite amount of energy to accelerate an object with mass to the speed of light. The speed of light is the upper limit for the speeds of objects with positive rest mass, and individual photons cannot travel faster than the speed of light. This is experimentally established in many tests of relativistic energy and momentum . More generally, it

9028-560: The first crewed spacecraft to orbit the Moon : for every question, the ground control station had to wait at least three seconds for the answer to arrive. The communications delay between Earth and Mars can vary between five and twenty minutes depending upon the relative positions of the two planets. As a consequence of this, if a robot on the surface of Mars were to encounter a problem, its human controllers would not be aware of it until approximately 4–24 minutes later. It would then take

9150-645: The galaxy. In space a few hundred light years from the Sun, deuterium abundance is only 15 atoms per million, but this value is presumably influenced by differential adsorption of deuterium onto carbon dust grains in interstellar space. The abundance of deuterium in Jupiter 's atmosphere has been directly measured by the Galileo space probe as 26 atoms per million hydrogen atoms. ISO-SWS observations find 22 atoms per million hydrogen atoms in Jupiter. and this abundance

9272-416: The group velocity to become infinite or negative, with pulses travelling instantaneously or backwards in time. None of these options allow information to be transmitted faster than c . It is impossible to transmit information with a light pulse any faster than the speed of the earliest part of the pulse (the front velocity). It can be shown that this is (under certain assumptions) always equal to c . It

9394-429: The individual crests and troughs of a plane wave (a wave filling the whole space, with only one frequency ) propagate is called the phase velocity   v p . A physical signal with a finite extent (a pulse of light) travels at a different speed. The overall envelope of the pulse travels at the group velocity   v g , and its earliest part travels at the front velocity   v f . The phase velocity

9516-453: The intermediate step of forming deuterium. Through much of the few minutes after the Big Bang during which nucleosynthesis could have occurred, the temperature was high enough that the mean energy per particle was greater than the binding energy of weakly bound deuterium; therefore, any deuterium that was formed was immediately destroyed. This situation is known as the deuterium bottleneck . The bottleneck delayed formation of any helium-4 until

9638-490: The introduction of isotopically enriched material into the substance, process or system under study. Isotope dilution involves adding enriched stable isotope to a substance in order to quantify the amount of that substance by measuring the resulting isotope ratios. Isotope labeling uses enriched isotope to label a substance in order to trace its progress through, for example, a chemical reaction, metabolic pathway or biological system. Some applications of isotope labeling rely on

9760-413: The isotopic differences in any other element. Bonds involving deuterium and tritium are somewhat stronger than the corresponding bonds in protium, and these differences are enough to cause significant changes in biological reactions. Pharmaceutical firms are interested in the fact that H is harder to remove from carbon than H. Deuterium can replace H in water molecules to form heavy water (H 2 O), which

9882-415: The long-lived radionuclides K , V , La , Lu also occur naturally.) Most odd–odd nuclei are unstable to beta decay , because the decay products are even–even , and thus more strongly bound, due to nuclear pairing effects . Deuterium, however, benefits from having its proton and neutron coupled to a spin-1 state, which gives a stronger nuclear attraction; the corresponding spin-1 state does not exist in

10004-404: The lower its energy. Therefore, the lowest possible energy state has s = 1 , l = 0 . In the second case the deuteron is a spin singlet, so that its total spin s is 0. It also has an odd parity and therefore odd orbital angular momentum l . Therefore, the lowest possible energy state has s = 0 , l = 1 . Since s = 1 gives a stronger nuclear attraction, the deuterium ground state

10126-502: The massive photon is described by Proca theory , the experimental upper bound for its mass is about 10 grams ; if photon mass is generated by a Higgs mechanism , the experimental upper limit is less sharp, m ≤ 10   eV/ c   (roughly 2 × 10  g). Another reason for the speed of light to vary with its frequency would be the failure of special relativity to apply to arbitrarily small scales, as predicted by some proposed theories of quantum gravity . In 2009,

10248-400: The measurement of stable isotope ratios to accomplish this. Speed of light The speed of light in vacuum , commonly denoted c , is a universal physical constant that is exactly equal to 299,792,458 metres per second (approximately 300,000 kilometres per second; 186,000 miles per second; 671 million miles per hour). According to the special theory of relativity , c is

10370-484: The motion of the source or the inertial reference frame of the observer . Particles with nonzero rest mass can be accelerated to approach c but can never reach it, regardless of the frame of reference in which their speed is measured. In the theory of relativity , c interrelates space and time and appears in the famous mass–energy equivalence , E = mc . In some cases, objects or waves may appear to travel faster than light (e.g., phase velocities of waves,

10492-585: The nuclear force. In both cases, this causes the diproton and dineutron to be unstable . The proton and neutron in deuterium can be dissociated through neutral current interactions with neutrinos . The cross section for this interaction is comparatively large, and deuterium was successfully used as a neutrino target in the Sudbury Neutrino Observatory experiment. Diatomic deuterium (H 2 ) has ortho and para nuclear spin isomers like diatomic hydrogen, but with differences in

10614-412: The nucleons. Since the proton and neutron have different values for g and g , one must separate their contributions. Each gets half of the deuterium orbital angular momentum l → {\displaystyle {\vec {l}}} and spin s → {\displaystyle {\vec {s}}} . One arrives at Stable isotope ratio Measurement of

10736-406: The number and population of spin states and rotational levels , which occur because the deuteron is a boson with nuclear spin equal to one. Due to the similarity in mass and nuclear properties between the proton and neutron, they are sometimes considered as two symmetric types of the same object, a nucleon . While only the proton has electric charge, this is often negligible due to the weakness of

10858-499: The observation of gamma-ray burst GRB 090510 found no evidence for a dependence of photon speed on energy, supporting tight constraints in specific models of spacetime quantization on how this speed is affected by photon energy for energies approaching the Planck scale . In a medium, light usually does not propagate at a speed equal to c ; further, different types of light wave will travel at different speeds. The speed at which

10980-421: The observer. This invariance of the speed of light was postulated by Einstein in 1905, after being motivated by Maxwell's theory of electromagnetism and the lack of evidence for motion against the luminiferous aether . It has since been consistently confirmed by many experiments. It is only possible to verify experimentally that the two-way speed of light (for example, from a source to a mirror and back again)

11102-505: The ocean: 4.85 × 10 tonnes of deuterium – mainly as HOD (or HOH or HHO) and only rarely as D 2 O (or H 2 O) (Deuterium Oxide, also known as Heavy Water )– in 1.4 × 10 tonnes of water. The abundance of H changes slightly from one kind of natural water to another (see Vienna Standard Mean Ocean Water ). The name deuterium comes from Greek deuteros , meaning "second". American chemist Harold Urey discovered deuterium in 1931. Urey and others produced samples of heavy water in which

11224-457: The only change as some of the radioactive products of Big Bang nucleosynthesis (such as tritium ) decay. The deuterium bottleneck in the formation of helium, together with the lack of stable ways for helium to combine with hydrogen or with itself (no stable nucleus has a mass number of 5 or 8) meant that an insignificant amount of carbon, or any elements heavier than carbon, formed in the Big Bang. These elements thus required formation in stars. At

11346-408: The other hand, some techniques depend on the finite speed of light, for example in distance measurements. In computers , the speed of light imposes a limit on how quickly data can be sent between processors . If a processor operates at 1   gigahertz , a signal can travel only a maximum of about 30 centimetres (1 ft) in a single clock cycle – in practice, this distance is even shorter since

11468-466: The outer solar atmosphere at roughly the same concentration as in Jupiter, and this has probably been unchanged since the origin of the Solar System. The natural abundance of H seems to be a very similar fraction of hydrogen, wherever hydrogen is found, unless there are obvious processes at work that concentrate it. The existence of deuterium at a low but constant primordial fraction in all hydrogen

11590-482: The oxygen isotope ratios. In addition, an unusual signature of carbon-13 confirms the non-terrestrial origin for organic compounds found in carbonaceous chondrites , as in the Murchison meteorite . The uses of stable isotope ratios described above pertain to measurements of naturally occurring ratios. Scientific research also relies on the measurement of stable isotope ratios that have been artificially perturbed by

11712-448: The oxygen isotopic composition of the water can be constrained. Paleotemperature relationships have also enabled isotope ratios from calcium carbonate in barnacle shells to be used to infer the movement and home foraging areas of the sea turtles and whales on which some barnacles grow. In ecology , carbon and nitrogen isotope ratios are widely used to determine the broad diets of many free-ranging animals. They have been used to determine

11834-490: The oxygen isotopic composition of the water. This oxygen remains "fixed" in the calcium carbonate when the foraminifera dies, falls to the sea bed, and its shell becomes part of the sediment. It is possible to select standard species of foraminifera from sections through the sediment column, and by mapping the variation in oxygen isotopic ratio, deduce the temperature that the Forminifera encountered during life if changes in

11956-420: The parameter  c is ubiquitous in modern physics, appearing in many contexts that are unrelated to light. For example, general relativity predicts that  c is also the speed of gravity and of gravitational waves , and observations of gravitational waves have been consistent with this prediction. In non-inertial frames of reference (gravitationally curved spacetime or accelerated reference frames ),

12078-403: The phase velocity is not the same for all the frequencies of the pulse) smears out over time, a process known as dispersion . Certain materials have an exceptionally low (or even zero) group velocity for light waves, a phenomenon called slow light . The opposite, group velocities exceeding c , was proposed theoretically in 1993 and achieved experimentally in 2000. It should even be possible for

12200-412: The photon has a mass have been considered. In such a theory, its speed would depend on its frequency, and the invariant speed  c of special relativity would then be the upper limit of the speed of light in vacuum. No variation of the speed of light with frequency has been observed in rigorous testing, putting stringent limits on the mass of the photon. The limit obtained depends on the model used: if

12322-404: The rare cluster decay , and occasional absorption of naturally occurring neutrons by light hydrogen, but these are trivial sources. There is thought to be little deuterium in the interior of the Sun and other stars, as at these temperatures the nuclear fusion reactions that consume deuterium happen much faster than the proton–proton reaction that creates deuterium. However, deuterium persists in

12444-496: The ratio of these two numbers, which is 1.000272. The wavelengths of all deuterium spectroscopic lines are shorter than the corresponding lines of light hydrogen, by 0.0272%. In astronomical observation, this corresponds to a blue Doppler shift of 0.0272% of the speed of light , or 81.6 km/s. The differences are much more pronounced in vibrational spectroscopy such as infrared spectroscopy and Raman spectroscopy , and in rotational spectra such as microwave spectroscopy because

12566-520: The ratios found in Earth seawater. The recent measurement of deuterium amounts of 161 atoms per million hydrogen in Comet 103P/Hartley (a former Kuiper belt object), a ratio almost exactly that in Earth's oceans (155.76 ± 0.1, but in fact from 153 to 156 ppm), emphasizes the theory that Earth's surface water may be largely from comets. Most recently the HHR of 67P/Churyumov–Gerasimenko as measured by Rosetta

12688-688: The ratios of naturally occurring stable isotopes ( isotope analysis ) plays an important role in isotope geochemistry , but stable isotopes (mostly hydrogen , carbon , nitrogen , oxygen and sulfur ) are also finding uses in ecological and biological studies. Other workers have used oxygen isotope ratios to reconstruct historical atmospheric temperatures, making them important tools for paleoclimatology . These isotope systems for lighter elements that exhibit more than one primordial isotope for each element have been under investigation for many years in order to study processes of isotope fractionation in natural systems. The long history of study of these elements

12810-614: The same time, the failure of much nucleogenesis during the Big Bang ensured that there would be plenty of hydrogen in the later universe available to form long-lived stars, such as the Sun. Deuterium occurs in trace amounts naturally as deuterium gas (H 2 or D 2 ), but most deuterium atoms in the Universe are bonded with H to form a gas called hydrogen deuteride (HD or HH). Similarly, natural water contains deuterated molecules, almost all as semiheavy water HDO with only one deuterium. The existence of deuterium on Earth, elsewhere in

12932-417: The speed v at which light travels in a material is called the refractive index n of the material ( n = ⁠ c / v ⁠ ). For example, for visible light, the refractive index of glass is typically around 1.5, meaning that light in glass travels at ⁠ c / 1.5 ⁠ ≈ 200 000  km/s ( 124 000  mi/s) ; the refractive index of air for visible light is about 1.0003, so

13054-470: The speed of light in air is about 90 km/s (56 mi/s) slower than c . The speed of light in vacuum is usually denoted by a lowercase c , for "constant" or the Latin celeritas (meaning 'swiftness, celerity'). In 1856, Wilhelm Eduard Weber and Rudolf Kohlrausch had used c for a different constant that was later shown to equal √ 2 times the speed of light in vacuum. Historically,

13176-479: The speed of light in vacuum. Since 1983, the constant c has been defined in the International System of Units (SI) as exactly 299 792 458  m/s ; this relationship is used to define the metre as exactly the distance that light travels in vacuum in 1 ⁄ 299 792 458 of a second. By using the value of c , as well as an accurate measurement of the second, one can thus establish

13298-470: The speed of light. A Global Positioning System (GPS) receiver measures its distance to GPS satellites based on how long it takes for a radio signal to arrive from each satellite, and from these distances calculates the receiver's position. Because light travels about 300 000  kilometres ( 186 000  miles ) in one second, these measurements of small fractions of a second must be very precise. The Lunar Laser Ranging experiment , radar astronomy and

13420-439: The speed of waves in any material medium, and c 0 for the speed of light in vacuum. This subscripted notation, which is endorsed in official SI literature, has the same form as related electromagnetic constants: namely, μ 0 for the vacuum permeability or magnetic constant, ε 0 for the vacuum permittivity or electric constant, and Z 0 for the impedance of free space . This article uses c exclusively for

13542-509: The spot is delayed because of the time it takes light to get to the distant object at the speed  c . However, the only physical entities that are moving are the laser and its emitted light, which travels at the speed  c from the laser to the various positions of the spot. Similarly, a shadow projected onto a distant object can be made to move faster than  c , after a delay in time. In neither case does any matter, energy, or information travel faster than light. The rate of change in

13664-407: The symbol V was used as an alternative symbol for the speed of light, introduced by James Clerk Maxwell in 1865. In 1894, Paul Drude redefined c with its modern meaning. Einstein used V in his original German-language papers on special relativity in 1905, but in 1907 he switched to c , which by then had become the standard symbol for the speed of light. Sometimes c is used for

13786-404: The system in these equations is close to the mass of a single electron, but differs from it by a small amount about equal to the ratio of mass of the electron to the nucleus. For H, this amount is about ⁠ 1837 / 1836 ⁠ , or 1.000545, and for H it is even smaller: ⁠ 3671 / 3670 ⁠ , or 1.0002725. The energies of electronic spectra lines for H and H therefore differ by

13908-471: The travel time increases when signals pass through electronic switches or signal regenerators. Although this distance is largely irrelevant for most applications, latency becomes important in fields such as high-frequency trading , where traders seek to gain minute advantages by delivering their trades to exchanges fractions of a second ahead of other traders. For example, traders have been switching to microwave communications between trading hubs, because of

14030-454: The two-neutron or two-proton system, due to the Pauli exclusion principle which would require one or the other identical particle with the same spin to have some other different quantum number, such as orbital angular momentum . But orbital angular momentum of either particle gives a lower binding energy for the system, mainly due to increasing distance of the particles in the steep gradient of

14152-475: The units of space and time), and requiring that physical theories satisfy a special symmetry called Lorentz invariance , whose mathematical formulation contains the parameter  c . Lorentz invariance is an almost universal assumption for modern physical theories, such as quantum electrodynamics , quantum chromodynamics , the Standard Model of particle physics , and general relativity . As such,

14274-529: The universe was less than a billion years old. The fact that more distant objects appear to be younger, due to the finite speed of light, allows astronomers to infer the evolution of stars , of galaxies , and of the universe itself. Astronomical distances are sometimes expressed in light-years , especially in popular science publications and media. A light-year is the distance light travels in one Julian year , around 9461 billion kilometres, 5879 billion miles, or 0.3066 parsecs . In round figures,

14396-493: The upper limit for the speed at which conventional matter or energy (and thus any signal carrying information ) can travel through space . All forms of electromagnetic radiation , including visible light , travel at the speed of light. For many practical purposes, light and other electromagnetic waves will appear to propagate instantaneously, but for long distances and very sensitive measurements, their finite speed has noticeable effects. Much starlight viewed on Earth

14518-436: The values of the electromagnetic constants ε 0 and μ 0 and using their relation to c . Historically, the most accurate results have been obtained by separately determining the frequency and wavelength of a light beam, with their product equalling c . This is described in more detail in the "Interferometry" section below. In 1983 the metre was defined as "the length of the path travelled by light in vacuum during

14640-627: The variation in certain isotope ratios in drugs derived from plant sources ( cannabis , cocaine ) can be used to determine the drug's continent of origin. In food science, stable isotope ratio analysis has been used to determine the composition of beer, shoyu sauce and dog food. Stable isotope ratio analysis also has applications in doping control , to distinguish between endogenous and exogenous ( synthetic ) sources of hormones . The accurate measurement of stable isotope ratios relies on proper procedures of analysis, sample preparation and storage. Chondrite meteorites are classified using

14762-498: Was farther away took longer to reach the Earth, the time between two successive observations corresponds to a longer time between the instants at which the light rays were emitted. A 2011 experiment where neutrinos were observed to travel faster than light turned out to be due to experimental error. In models of the expanding universe , the farther galaxies are from each other, the faster they drift apart. For example, galaxies far away from Earth are inferred to be moving away from

14884-557: Was shut down. Canada uses heavy water as a neutron moderator for the operation of the CANDU reactor design. Another major producer of heavy water is India. All but one of India's atomic energy plants are pressurized heavy water plants, which use natural (i.e., not enriched) uranium. India has eight heavy water plants, of which seven are in operation. Six plants, of which five are in operation, are based on D–H exchange in ammonia gas. The other two plants extract deuterium from natural water in

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