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20,200 | The Allison engine in the Mustang I had a single-stage supercharger that caused power to drop off rapidly above . This made it unsuitable for use at the altitudes where combat was taking place in Europe. Allison’s attempts at developing a high-altitude engine were underfunded, but produced the V-1710-45, which featured... | https://en.wikipedia.org/wiki?curid=24710 |
20,201 | At the same time, the possibility of combining the P-51 airframe with the US license-built Packard version of the Merlin engine was being explored on the other side of the Atlantic. In July 1942, a contract was let for two prototypes, briefly designated XP-78, but soon to become the XP-51B. Based on the Packard V-1650-... | https://en.wikipedia.org/wiki?curid=24710 |
20,202 | The Mustang was initially developed for the RAF, which was its first user. As the first Mustangs were built to British requirements, these aircraft used factory numbers and were not P-51s; the order comprised 320 NA-73s, followed by 300 NA-83s, all of which were designated North American Mustang Mark I by the RAF. The ... | https://en.wikipedia.org/wiki?curid=24710 |
20,203 | After the arrival of the initial aircraft in the UK in October 1941, the first squadron of Mustang Mk Is entered service in January 1942, the first being No. 26 Squadron RAF. Due to poor high-altitude performance, the Mustangs were used by Army Co-operation Command, rather than Fighter Command, and were used for tactic... | https://en.wikipedia.org/wiki?curid=24710 |
20,204 | Army Co-operation Command used the Mustang’s superior speed and long range to conduct low-altitude “Rhubarb” raids over continental Europe, sometimes penetrating German airspace. The V-1710 engine ran smoothly at 1,100 rpm, versus 1,600 for the Merlin, enabling long flights over water at altitude before approaching the... | https://en.wikipedia.org/wiki?curid=24710 |
20,205 | The RAF also operated 308 P-51Bs and 636 P-51Cs, which were known in RAF service as Mustang Mk IIIs; the first units converted to the type in late 1943 and early 1944. Mustang Mk III units were operational until the end of World War II, though many units had already converted to the Mustang Mk IV (P-51D) and Mk IVa (P-... | https://en.wikipedia.org/wiki?curid=24710 |
20,206 | Prewar doctrine was based on the idea "the bomber will always get through". Despite RAF and Luftwaffe experience with daylight bombing, the USAAF still incorrectly believed in 1942 that tightly packed formations of bombers would have so much firepower that they could fend off fighters on their own. Fighter escort was a... | https://en.wikipedia.org/wiki?curid=24710 |
20,207 | The 8th Air Force started operations from Britain in August 1942. At first, because of the limited scale of operations, no conclusive evidence showed American doctrine was failing. In the 26 operations flown to the end of 1942, the loss rate had been under 2%. | https://en.wikipedia.org/wiki?curid=24710 |
20,208 | In January 1943, at the Casablanca Conference, the Allies formulated the Combined Bomber Offensive (CBO) plan for "round-the-clock" bombing – USAAF daytime operations complementing the RAF nighttime raids on industrial centers. In June 1943, the Combined Chiefs of Staff issued the Pointblank Directive to destroy the Lu... | https://en.wikipedia.org/wiki?curid=24710 |
20,209 | For the US, the very concept of self-defending bombers was called into question, but instead of abandoning daylight raids and turning to night bombing, as the RAF suggested, they chose other paths; at first, bombers converted to gunships (the Boeing YB-40) was believed to be able to escort the bomber formations, but wh... | https://en.wikipedia.org/wiki?curid=24710 |
20,210 | The P-51 Mustang was a solution to the need for an effective bomber escort. It used a common, reliable engine and had internal space for a larger-than-average fuel load. With external fuel tanks, it could accompany the bombers from England to Germany and back. | https://en.wikipedia.org/wiki?curid=24710 |
20,211 | By the time the Pointblank offensive resumed in early 1944, matters had changed. Bomber escort defenses were initially layered, using the shorter-range P-38s and P-47s to escort the bombers during the initial stages of the raid before handing over to the P-51s when they were forced to turn for home. This provided conti... | https://en.wikipedia.org/wiki?curid=24710 |
20,212 | The Luftwaffe's twin-engined Messerschmitt Bf 110 heavy fighters brought up to deal with the bombers proved to be easy prey for the Mustangs, and had to be quickly withdrawn from combat. The Focke-Wulf Fw 190A, already suffering from poor high-altitude performance, was outperformed by the Mustang at the B-17's altitude... | https://en.wikipedia.org/wiki?curid=24710 |
20,213 | At the start of 1944, Major General James Doolittle, the new commander of the 8th Air Force, released most fighters from the requirement of flying in close formation with the bombers, allowing them free rein to attack the Luftwaffe wherever it could be found. The aim was to achieve air supremacy. Mustang groups were se... | https://en.wikipedia.org/wiki?curid=24710 |
20,214 | The Luftwaffe answered with the "Gefechtsverband" ("battle formation"). This consisted of a "Sturmgruppe" of heavily armed and armored Fw 190 As escorted by two "Begleitgruppen" of Messerschmitt Bf 109s, whose task was to keep the Mustangs away from the Fw 190 as they attacked the bombers. This strategy proved to be pr... | https://en.wikipedia.org/wiki?curid=24710 |
20,215 | While not always able to avoid contact with the escorts, the threat of mass attacks and later the "company front" (eight abreast) assaults by armored "Sturmgruppe" Fw 190As brought an urgency to attacking the Luftwaffe wherever it could be found, either in the air or on the ground. Beginning in late February 1944, 8th ... | https://en.wikipedia.org/wiki?curid=24710 |
20,216 | The numerical superiority of the USAAF fighters, superb flying characteristics of the P-51, and pilot proficiency helped cripple the Luftwaffe's fighter force. As a result, the fighter threat to the US, and later British, bombers was greatly diminished by July 1944. The RAF, long proponents of night bombing for protect... | https://en.wikipedia.org/wiki?curid=24710 |
20,217 | On 15 April 1944, VIII Fighter Command began "Operation Jackpot", attacks on Luftwaffe fighter airfields. As the efficacy of these missions increased, the number of fighters at the German airbases fell to the point where they were no longer considered worthwhile targets. On 21 May, targets were expanded to include rail... | https://en.wikipedia.org/wiki?curid=24710 |
20,218 | Given the overwhelming Allied air superiority, the Luftwaffe put its effort into the development of aircraft of such high performance that they could operate with impunity, but which also made bomber attack much more difficult, merely from the flight velocities they achieved. Foremost among these were the Messerschmitt... | https://en.wikipedia.org/wiki?curid=24710 |
20,219 | The Mustang also proved useful against the V-1s launched toward London. P-51B/Cs using 150-octane fuel were fast enough to catch the V-1 and operated in concert with shorter-range aircraft such as advanced marks of the Supermarine Spitfire and Hawker Tempest. | https://en.wikipedia.org/wiki?curid=24710 |
20,220 | By 8 May 1945, the 8th, 9th, and 15th Air Force's P-51 groups claimed some 4,950 aircraft shot down (about half of all USAAF claims in the European theater, the most claimed by any Allied fighter in air-to-air combat) and 4,131 destroyed on the ground. Losses were about 2,520 aircraft. The 8th Air Force's 4th Fighter G... | https://en.wikipedia.org/wiki?curid=24710 |
20,221 | In air combat, the top-scoring P-51 units (both of which exclusively flew Mustangs) were the 357th Fighter Group of the 8th Air Force with 565 air-to-air combat victories and the 9th Air Force's 354th Fighter Group with 664, which made it one of the top-scoring fighter groups. The top Mustang ace was the USAAF's George... | https://en.wikipedia.org/wiki?curid=24710 |
20,222 | In early 1945, P-51C, D, and K variants also joined the Chinese Nationalist Air Force. These Mustangs were provided to the 3rd, 4th, and 5th Fighter Groups and used to attack Japanese targets in occupied areas of China. The P-51 became the most capable fighter in China, while the Imperial Japanese Army Air Force used t... | https://en.wikipedia.org/wiki?curid=24710 |
20,223 | The P-51 was a relative latecomer to the Pacific Theater, due largely to the need for the aircraft in Europe, although the P-38's twin-engined design was considered a safety advantage for long, over-water flights. The first P-51s were deployed in the Far East later in 1944, operating in close-support and escort mission... | https://en.wikipedia.org/wiki?curid=24710 |
20,224 | The command's last major raid of May was a daylight incendiary attack on Yokohama on 29 May conducted by 517 B-29s escorted by 101 P-51s. This force was intercepted by 150 A6M Zero fighters, sparking an intense air battle in which five B-29s were shot down and another 175 damaged. In return, the P-51 pilots claimed 26 ... | https://en.wikipedia.org/wiki?curid=24710 |
20,225 | P-51s also conducted a series of independent ground-attack missions against targets in the home islands. The first of these operations took place on 16 April, when 57 P-51s strafed Kanoya Air Field in Kyushu. In operations conducted between 26 April and 22 June, the American fighter pilots claimed the destruction of 64... | https://en.wikipedia.org/wiki?curid=24710 |
20,226 | Due to the lack of Japanese air opposition to the American bomber raids, VII Fighter Command was solely tasked with ground-attack missions from July. These raids were frequently made against airfields to destroy aircraft being held in reserve to attack the expected Allied invasion fleet. While the P-51 pilots only occa... | https://en.wikipedia.org/wiki?curid=24710 |
20,227 | Chief Naval Test Pilot and C.O. Captured Enemy Aircraft Flight Capt. Eric Brown, CBE, DSC, AFC, RN, tested the Mustang at RAE Farnborough in March 1944 and noted: | https://en.wikipedia.org/wiki?curid=24710 |
20,228 | Kurt Bühligen, the third-highest scoring German fighter pilot of World War II's Western Front (with 112 confirmed victories, three against Mustangs), later stated: | https://en.wikipedia.org/wiki?curid=24710 |
20,229 | In the aftermath of World War II, the USAAF consolidated much of its wartime combat force and selected the P-51 as a "standard" piston-engined fighter, while other types, such as the P-38 and P-47, were withdrawn or given substantially reduced roles. As the more advanced (P-80 and P-84) jet fighters were introduced, th... | https://en.wikipedia.org/wiki?curid=24710 |
20,230 | In 1947, the newly formed USAF Strategic Air Command employed Mustangs alongside F-6 Mustangs and F-82 Twin Mustangs, due to their range capabilities. In 1948, the designation P-51 (P for pursuit) was changed to F-51 (F for fighter) and the existing F designator for photographic reconnaissance aircraft was dropped beca... | https://en.wikipedia.org/wiki?curid=24710 |
20,231 | From the start of the Korean War, the Mustang once again proved useful. A "substantial number" of stored or in-service F-51Ds were shipped, via aircraft carriers, to the combat zone, and were used by the USAF, the South African Air Force, and the Republic of Korea Air Force (ROKAF). The F-51 was used for ground attack,... | https://en.wikipedia.org/wiki?curid=24710 |
20,232 | Mustangs continued flying with USAF and ROKAF fighter-bomber units on close support and interdiction missions in Korea until 1953 when they were largely replaced as fighter-bombers by USAF F-84s and by United States Navy (USN) Grumman F9F Panthers. Other air forces and units using the Mustang included the Royal Austral... | https://en.wikipedia.org/wiki?curid=24710 |
20,233 | F-51s flew in the Air Force Reserve and ANG throughout the 1950s. The last American USAF Mustang was F-51D-30-NA AF serial no. 44-74936, which was finally withdrawn from service with the West Virginia Air National Guard's 167th Fighter Interceptor Squadron in January 1957 and retired to what was then called the Air For... | https://en.wikipedia.org/wiki?curid=24710 |
20,234 | The final withdrawal of the Mustang from USAF dumped hundreds of P-51s onto the civilian market. The rights to the Mustang design were purchased from North American by the Cavalier Aircraft Corporation, which attempted to market the surplus Mustang aircraft in the U.S. and overseas. In 1967 and again in 1972, the USAF ... | https://en.wikipedia.org/wiki?curid=24710 |
20,235 | The last U.S. military use of the F-51 was in 1968 when the U. S. Army employed a vintage F-51D (44-72990) as a chase aircraft for the Lockheed YAH-56 Cheyenne armed helicopter project. This aircraft was so successful that the Army ordered two F-51Ds from Cavalier in 1968 for use at Fort Rucker as chase planes. They we... | https://en.wikipedia.org/wiki?curid=24710 |
20,236 | The F-51 was adopted by many foreign air forces and continued to be an effective fighter into the mid-1980s with smaller air arms. The last Mustang ever downed in battle occurred during Operation Power Pack in the Dominican Republic in 1965, with the last aircraft finally being retired by the Dominican Air Force in 198... | https://en.wikipedia.org/wiki?curid=24710 |
20,237 | After World War II, the P-51 Mustang served in the air arms of more than 25 nations. During the war, a Mustang cost about $51,000, while many hundreds were sold postwar for the nominal price of one dollar to signatories of the Inter-American Treaty of Reciprocal Assistance, ratified in Rio de Janeiro in 1947. | https://en.wikipedia.org/wiki?curid=24710 |
20,238 | Many P-51s were sold as surplus after the war, often for as little as $1,500. Some were sold to former wartime fliers or other aficionados for personal use, while others were modified for air racing. | https://en.wikipedia.org/wiki?curid=24710 |
20,239 | One of the most significant Mustangs involved in air racing was serial number 44-10947, a surplus P-51C-10-NT purchased by film stunt pilot Paul Mantz. He modified the wings, sealing them to create a giant fuel tank in each one; these "wet wings" reduced the need for fuel stops or drag-inducing drop tanks. Named "Blaze... | https://en.wikipedia.org/wiki?curid=24710 |
20,240 | In 1958, the RCAF retired its 78 remaining Mustangs. RCAF pilot Lynn Garrison ferried them from their various storage locations to Canastota, New York, where the American buyers were based. Garrison flew each of the surviving aircraft at least once. These aircraft make up a large percentage of the aircraft presently fl... | https://en.wikipedia.org/wiki?curid=24710 |
20,241 | The most prominent firm to convert Mustangs to civilian use was Trans-Florida Aviation, later renamed Cavalier Aircraft Corporation, which produced the Cavalier Mustang. Modifications included a taller tailfin and wingtip tanks. A number of conversions included a Cavalier Mustang specialty: a "tight" second seat added ... | https://en.wikipedia.org/wiki?curid=24710 |
20,242 | In the late 1960s and early 1970s, when the United States Department of Defense wished to supply aircraft to South American countries and later Indonesia for close air support and counterinsurgency, it paid Cavalier to return some of their civilian conversions back to updated military specifications. | https://en.wikipedia.org/wiki?curid=24710 |
20,243 | In the 21st century, a P-51 can command a price of more than $1 million, even for only partially restored aircraft. There were 204 privately owned P-51s in the U.S. on the FAA registry in 2011, most of which are still flying, often associated with organizations such as the Commemorative Air Force (formerly the Confeder... | https://en.wikipedia.org/wiki?curid=24710 |
20,244 | In May 2013, Doug Matthews set an altitude record of in a P-51 named "The Rebel" for piston-powered aircraft weighing . Flying from a grass runway at Florida's Indiantown airport and over Lake Okeechobee, Matthews set world records for time to reach altitudes of , 18 minutes and , 31 minutes. He set a level-flight alti... | https://en.wikipedia.org/wiki?curid=24710 |
20,245 | Except for the small numbers assembled or produced in Australia, all Mustangs were built by North American initially at Inglewood, California, but then additionally in Dallas, Texas. | https://en.wikipedia.org/wiki?curid=24710 |
20,246 | As indicative of the iconic nature of the P-51, manufacturers within the hobby industry have created scale plastic model kits of the P-51 Mustang, with varying degrees of detail and skill levels. The aircraft have also been the subject of numerous scale flying replicas. Aside from the popular radio-controlled aircraft,... | https://en.wikipedia.org/wiki?curid=24710 |
20,247 | The Planck constant, or Planck's constant, is a fundamental physical constant of foundational importance in quantum mechanics. The constant gives the relationship between the energy of a photon and its frequency, and by the mass-energy equivalence, the relationship between mass and frequency. Specifically, a photon's e... | https://en.wikipedia.org/wiki?curid=19594213 |
20,248 | In metrology it is used, together with other constants, to define the kilogram, the SI unit of mass. The SI units are defined in such a way that, when the Planck constant is expressed in SI units, it has the exact value | https://en.wikipedia.org/wiki?curid=19594213 |
20,249 | The constant was first postulated by Max Planck in 1900 as part of a solution to the ultraviolet catastrophe. At the end of the 19th century, accurate measurements of the spectrum of black body radiation existed, but the distribution of those measurements at higher frequencies diverged significantly from what was predi... | https://en.wikipedia.org/wiki?curid=19594213 |
20,250 | In 1905, Albert Einstein determined a "quantum" or minimal element of the energy of the electromagnetic wave itself. The light quantum behaved in some respects as an electrically neutral particle, and was eventually called a photon. Max Planck received the 1918 Nobel Prize in Physics "in recognition of the services he ... | https://en.wikipedia.org/wiki?curid=19594213 |
20,251 | Planck's constant was formulated as part of Max Planck's successful effort to produce a mathematical expression that accurately predicted the observed spectral distribution of thermal radiation from a closed furnace (black-body radiation). This mathematical expression is now known as Planck's law. | https://en.wikipedia.org/wiki?curid=19594213 |
20,252 | In the last years of the 19th century, Max Planck was investigating the problem of black-body radiation first posed by Kirchhoff some 40 years earlier. Every physical body spontaneously and continuously emits electromagnetic radiation. There was no expression or explanation for the overall shape of the observed emissio... | https://en.wikipedia.org/wiki?curid=19594213 |
20,253 | Approaching this problem, Planck hypothesized that the equations of motion for light describe a set of harmonic oscillators, one for each possible frequency. He examined how the entropy of the oscillators varied with the temperature of the body, trying to match Wien's law, and was able to derive an approximate mathemat... | https://en.wikipedia.org/wiki?curid=19594213 |
20,254 | Planck tried to find a mathematical expression that could reproduce Wien's law (for short wavelengths) and the empirical formula (for long wavelengths). This expression included a constant, formula_4, which is thought to be for Hilfsgrösse (auxiliary variable), and subsequently became known as the Planck constant. The ... | https://en.wikipedia.org/wiki?curid=19594213 |
20,255 | where formula_6 is the Boltzmann constant, formula_4 is the Planck constant, and formula_8 is the speed of light in the medium, whether material or vacuum. | https://en.wikipedia.org/wiki?curid=19594213 |
20,256 | The spectral radiance of a body, formula_9, describes the amount of energy it emits at different radiation frequencies. It is the power emitted per unit area of the body, per unit solid angle of emission, per unit frequency. The spectral radiance can also be expressed per unit wavelength formula_10 instead of per unit ... | https://en.wikipedia.org/wiki?curid=19594213 |
20,257 | showing how radiated energy emitted at shorter wavelengths increases more rapidly with temperature than energy emitted at longer wavelengths. | https://en.wikipedia.org/wiki?curid=19594213 |
20,258 | Planck's law may also be expressed in other terms, such as the number of photons emitted at a certain wavelength, or the energy density in a volume of radiation. The SI units of formula_9 are , while those of formula_13 are . | https://en.wikipedia.org/wiki?curid=19594213 |
20,259 | Planck soon realized that his solution was not unique. There were several different solutions, each of which gave a different value for the entropy of the oscillators. To save his theory, Planck resorted to using the then-controversial theory of statistical mechanics, which he described as "an act of despair … I was re... | https://en.wikipedia.org/wiki?curid=19594213 |
20,260 | With this new condition, Planck had imposed the quantization of the energy of the oscillators, "a purely formal assumption … actually I did not think much about it ..." in his own words, but one that would revolutionize physics. Applying this new approach to Wien's displacement law showed that the "energy element" must... | https://en.wikipedia.org/wiki?curid=19594213 |
20,261 | Planck was able to calculate the value of formula_15 from experimental data on black-body radiation: his result, , is within 1.2% of the currently accepted value. He also made the first determination of the Boltzmann constant formula_6 from the same data and theory. | https://en.wikipedia.org/wiki?curid=19594213 |
20,262 | The black-body problem was revisited in 1905, when Lord Rayleigh and James Jeans (on the one hand) and Albert Einstein (on the other hand) independently proved that classical electromagnetism could "never" account for the observed spectrum. These proofs are commonly known as the "ultraviolet catastrophe", a name coined... | https://en.wikipedia.org/wiki?curid=19594213 |
20,263 | The photoelectric effect is the emission of electrons (called "photoelectrons") from a surface when light is shone on it. It was first observed by Alexandre Edmond Becquerel in 1839, although credit is usually reserved for Heinrich Hertz, who published the first thorough investigation in 1887. Another particularly thor... | https://en.wikipedia.org/wiki?curid=19594213 |
20,264 | Before Einstein's paper, electromagnetic radiation such as visible light was considered to behave as a wave: hence the use of the terms "frequency" and "wavelength" to characterize different types of radiation. The energy transferred by a wave in a given time is called its intensity. The light from a theatre spotlight ... | https://en.wikipedia.org/wiki?curid=19594213 |
20,265 | The "photoelectrons" emitted as a result of the photoelectric effect have a certain kinetic energy, which can be measured. This kinetic energy (for each photoelectron) is "independent" of the intensity of the light, but depends linearly on the frequency; and if the frequency is too low (corresponding to a photon energy... | https://en.wikipedia.org/wiki?curid=19594213 |
20,266 | Einstein's explanation for these observations was that light itself is quantized; that the energy of light is not transferred continuously as in a classical wave, but only in small "packets" or quanta. The size of these "packets" of energy, which would later be named photons, was to be the same as Planck's "energy elem... | https://en.wikipedia.org/wiki?curid=19594213 |
20,267 | Einstein's postulate was later proven experimentally: the constant of proportionality between the frequency of incident light formula_18 and the kinetic energy of photoelectrons formula_19 was shown to be equal to the Planck constant formula_15. | https://en.wikipedia.org/wiki?curid=19594213 |
20,268 | It was John William Nicholson in 1912 who introduced h-bar into the theory of the atom which was the first quantum and nuclear atom and the first to quantize angular momentum as "h"/2. Niels Bohr quoted him in his 1913 paper of the Bohr model of the atom. The influence of the work of Nicholson’s nuclear quantum atomic ... | https://en.wikipedia.org/wiki?curid=19594213 |
20,269 | Niels Bohr introduced the third quantized model of the atom in 1913, in an attempt to overcome a major shortcoming of Rutherford's classical model. The first quantized model of the atom was introduced in 1910 by Arthur Erich Haas and was discussed at the 1911 Solvay conference. In classical electrodynamics, a charge mo... | https://en.wikipedia.org/wiki?curid=19594213 |
20,270 | where formula_23 is the speed of light in vacuum, formula_24 is an experimentally determined constant (the Rydberg constant) and formula_25. Once the electron reached the lowest energy level (formula_26), it could not get any closer to the nucleus (lower energy). This approach also allowed Bohr to account for the Rydbe... | https://en.wikipedia.org/wiki?curid=19594213 |
20,271 | Bohr also introduced the quantity formula_28, now known as the reduced Planck constant or Dirac constant, as the quantum of angular momentum. At first, Bohr thought that this was the angular momentum of each electron in an atom: this proved incorrect and, despite developments by Sommerfeld and others, an accurate descr... | https://en.wikipedia.org/wiki?curid=19594213 |
20,272 | The Planck constant also occurs in statements of Werner Heisenberg's uncertainty principle. Given numerous particles prepared in the same state, the uncertainty in their position, formula_32, and the uncertainty in their momentum, formula_33, obey | https://en.wikipedia.org/wiki?curid=19594213 |
20,273 | where the uncertainty is given as the standard deviation of the measured value from its expected value. There are several other such pairs of physically measurable conjugate variables which obey a similar rule. One example is time vs. energy. The inverse relationship between the uncertainty of the two conjugate variabl... | https://en.wikipedia.org/wiki?curid=19594213 |
20,274 | In addition to some assumptions underlying the interpretation of certain values in the quantum mechanical formulation, one of the fundamental cornerstones to the entire theory lies in the commutator relationship between the position operator formula_35 and the momentum operator formula_36: | https://en.wikipedia.org/wiki?curid=19594213 |
20,275 | Since the frequency , wavelength , and speed of light are related by formula_40, the relation can also be expressed as | https://en.wikipedia.org/wiki?curid=19594213 |
20,276 | In 1923, Louis de Broglie generalized the Planck–Einstein relation by postulating that the Planck constant represents the proportionality between the momentum and the quantum wavelength of not just the photon, but the quantum wavelength of any particle. This was confirmed by experiments soon afterward. This holds throu... | https://en.wikipedia.org/wiki?curid=19594213 |
20,277 | These two relations are the temporal and spatial parts of the special relativistic expression using 4-vectors. | https://en.wikipedia.org/wiki?curid=19594213 |
20,278 | Classical statistical mechanics requires the existence of (but does not define its value). Eventually, following upon Planck's discovery, it was speculated that physical action could not take on an arbitrary value, but instead was restricted to integer multiples of a very small quantity, the "[elementary] quantum of ac... | https://en.wikipedia.org/wiki?curid=19594213 |
20,279 | In many cases, such as for monochromatic light or for atoms, quantization of energy also implies that only certain energy levels are allowed, and values in between are forbidden. | https://en.wikipedia.org/wiki?curid=19594213 |
20,280 | Implicit in the dimensions of the Planck constant is the fact that the SI unit of frequency, the hertz, represents one complete cycle, 360 degrees or radians, per second. | https://en.wikipedia.org/wiki?curid=19594213 |
20,281 | In applications where it is natural to use the angular frequency (i.e. where the frequency is expressed in terms of radians per second instead of cycles per second or hertz) it is often useful to absorb a factor of into the Planck constant. The resulting constant is called the reduced Planck constant or Dirac constant.... | https://en.wikipedia.org/wiki?curid=19594213 |
20,282 | The Planck constant has dimensions of angular momentum. In SI units, the Planck constant is expressed with the unit joule per hertz (J⋅Hz) or joule-second (J⋅s). | https://en.wikipedia.org/wiki?curid=19594213 |
20,283 | Since 2019, the numerical value of the Planck constant has been fixed, with a finite decimal representation. Under the present definition of the kilogram, which states that "The kilogram [...] is defined by taking the fixed numerical value of to be when expressed in the unit J⋅s, which is equal to kg⋅m⋅s, where the met... | https://en.wikipedia.org/wiki?curid=19594213 |
20,284 | As an illustration of this, suppose the decision of making to be exact was taken in 2010, when its measured value was , thus the present definition of kilogram was also enforced. In the future, the value of one kilogram must be refined to times the mass of the International Prototype of the Kilogram (IPK). | https://en.wikipedia.org/wiki?curid=19594213 |
20,285 | The Planck constant is related to the quantization of light and matter. It can be seen as a subatomic-scale constant. In a unit system adapted to subatomic scales, the electronvolt is the appropriate unit of energy and the petahertz the appropriate unit of frequency. Atomic unit systems are based (in part) on the Planc... | https://en.wikipedia.org/wiki?curid=19594213 |
20,286 | The Planck constant is one of the smallest constants used in physics. This reflects the fact that on a scale adapted to humans, where energies are typical of the order of kilojoules and times are typical of the order of seconds or minutes, the Planck constant is very small. One can regard the Planck constant to be only... | https://en.wikipedia.org/wiki?curid=19594213 |
20,287 | Equivalently, the order of the Planck constant reflects the fact that everyday objects and systems are made of a "large" number of microscopic particles. For example, green light with a wavelength of 555 nanometres (a wavelength that can be perceived by the human eye to be green) has a frequency of (). Each photon has ... | https://en.wikipedia.org/wiki?curid=19594213 |
20,288 | In principle, the Planck constant can be determined by examining the spectrum of a black-body radiator or the kinetic energy of photoelectrons, and this is how its value was first calculated in the early twentieth century. In practice, these are no longer the most accurate methods. | https://en.wikipedia.org/wiki?curid=19594213 |
20,289 | Since the value of the Planck constant is fixed now, it is no longer determined or calculated in laboratories. Some of the practices given below to determine the Planck constant are now used to determine the mass of the kilogram. All of the methods given below "except" the X-ray crystal density method rely on the theor... | https://en.wikipedia.org/wiki?curid=19594213 |
20,290 | The Josephson constant "K" relates the potential difference "U" generated by the Josephson effect at a "Josephson junction" with the frequency "ν" of the microwave radiation. The theoretical treatment of Josephson effect suggests very strongly that . | https://en.wikipedia.org/wiki?curid=19594213 |
20,291 | The Josephson constant may be measured by comparing the potential difference generated by an array of Josephson junctions with a potential difference which is known in SI volts. The measurement of the potential difference in SI units is done by allowing an electrostatic force to cancel out a measurable gravitational fo... | https://en.wikipedia.org/wiki?curid=19594213 |
20,292 | A Kibble balance (formerly known as a watt balance) is an instrument for comparing two powers, one of which is measured in SI watts and the other of which is measured in conventional electrical units. From the definition of the "conventional" watt "W", this gives a measure of the product "K""R" in SI units, where "R" i... | https://en.wikipedia.org/wiki?curid=19594213 |
20,293 | The gyromagnetic ratio "γ" of an object is the ratio of its magnetic moment to its angular momentum, which is directly related to the constant of proportionality between the frequency "ν" of nuclear magnetic resonance (or electron paramagnetic resonance for electrons) and the applied magnetic field "B": . It is difficu... | https://en.wikipedia.org/wiki?curid=19594213 |
20,294 | The ratio of the shielded proton magnetic moment "μ"′ to the electron magnetic moment "μ" can be measured separately and to high precision, as the imprecisely known value of the applied magnetic field cancels itself out in taking the ratio. The value of "μ" in Bohr magnetons is also known: it is half the electron "g"-f... | https://en.wikipedia.org/wiki?curid=19594213 |
20,295 | A further complication is that the measurement of "γ"′ involves the measurement of an electric current: this is invariably measured in "conventional" amperes rather than in SI amperes, so a conversion factor is required. The symbol Γ′ is used for the measured gyromagnetic ratio using conventional electrical units. In a... | https://en.wikipedia.org/wiki?curid=19594213 |
20,296 | The Faraday constant "F" is the charge of one mole of electrons, equal to the Avogadro constant "N" multiplied by the elementary charge "e". It can be determined by careful electrolysis experiments, measuring the amount of silver dissolved from an electrode in a given time and for a given electric current. Substituting... | https://en.wikipedia.org/wiki?curid=19594213 |
20,297 | The X-ray crystal density method is primarily a method for determining the Avogadro constant "N" but as the Avogadro constant is related to the Planck constant it also determines a value for "h". The principle behind the method is to determine "N" as the ratio between the volume of the unit cell of a crystal, measured ... | https://en.wikipedia.org/wiki?curid=19594213 |
20,298 | The experimental measurement of the Planck constant in the Large Hadron Collider laboratory was carried out in 2011. | https://en.wikipedia.org/wiki?curid=19594213 |
20,299 | A myocardial infarction (MI), commonly known as a heart attack, occurs when blood flow decreases or stops to the coronary artery of the heart, causing damage to the heart muscle. The most common symptom is chest pain or discomfort which may travel into the shoulder, arm, back, neck or jaw. Often it occurs in the center... | https://en.wikipedia.org/wiki?curid=20556798 |
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