U+210F PLANCK CONSTANT OVER TWO PI

U+210F was added to Unicode in version 1.1 (1993). It belongs to the block Letterlike Symbols in the Basic Multilingual Plane.

This character is a Lowercase Letter and is commonly used, that is, in no specific script.

The glyph is a Font composition of the glyphs . It has a Neutral East Asian Width. In bidirectional context it acts as Left To Right and is not mirrored. The glyph can, under circumstances, be confused with 2 other glyphs. In text U+210F behaves as Alphabetic regarding line breaks. It has type Lower for sentence and ALetter for word breaks. The Grapheme Cluster Break is Any.

The Planck constant (denoted h, also called Planck's constant) is a physical constant that is the quantum of action in quantum mechanics. Published in 1900, it originally described the proportionality constant between the energy, E, of a charged atomic oscillator in the wall of a black body, and the frequency, ν, of its associated electromagnetic wave. Its relevance is now integral to the field of quantum mechanics, describing the relationship between energy and frequency, known as the Planck–Einstein relation:

In 1905 the value E, the energy of a charged atomic oscillator, was theoretically associated with the energy of the electromagnetic wave itself, representing the minimum amount of energy required to form an electromagnetic field (a "quantum"). Further investigation of quanta revealed behaviour associated with an independent unit ("particle") as opposed to an electromagnetic wave and was eventually given the term photon. The Planck–Einstein relation now describes the energy of each photon in terms of the photon's frequency. This energy is extremely small in terms of ordinary experience.

Since the frequency ν, wavelength λ, and speed of light c are related by λν = c, the Planck–Einstein relation for a photon can also be expressed as

The above equation leads to another relationship involving the Planck constant. Given p for the linear momentum of a particle (not only a photon, but other particles as well), the de Broglie wavelength λ of the particle is given by

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 rotations per second or Hertz) it is often useful to absorb a factor of 2π into the Planck constant. The resulting constant is called the reduced Planck constant or Dirac constant. It is equal to the Planck constant divided by 2π, and is denoted ħ (pronounced "h-bar"):

The energy of a photon or particle with angular frequency ω, where ω = 2πν, is given by

while its linear momentum relates to

This holds for all fields of wave mechanics, including the electrodynamics and quantum mechanics.

The Planck constant is named after Max Planck, the instigator of quantum theory, who discovered it in 1900. Classical statistical mechanics requires the existence of h (but does not define its value). Planck discovered that physical action could not take on an arbitrary value. Instead, the action must be some multiple of a very small quantity (later to be named the "quantum of action" and now called Planck constant). This inherent granularity is counterintuitive in the everyday world, where it is possible to "make things a little bit hotter" or "move things a little bit faster". This is because the quanta of action are very, very small in comparison to everyday macroscopic human experience. Hence, the granularity of nature appears smooth to us.

Thus, on the macroscopic scale, quantum mechanics and classical physics converge at the classical limit. Nevertheless, it is impossible, as Planck discovered, to explain some phenomena without accepting the fact that action is quantized. In many cases, such as for monochromatic light or for atoms, this quantum of action also implies that only certain energy levels are allowed, and values in between are forbidden. 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 afterwards.

Representations

System Representation
8463
UTF-8 E2 84 8F
UTF-16 21 0F
UTF-32 00 00 21 0F
URL-Quoted %E2%84%8F
HTML-Escape &#x210F;
Wrong windows-1252 Mojibake â
HTML-Escape &hbar;
HTML-Escape &hslash;
HTML-Escape &planck;
HTML-Escape &plankv;
LaTeX \hslash

Complete Record

Property Value
Age (age) 1.1
Unicode Name (na) PLANCK CONSTANT OVER TWO PI
Unicode 1 Name (na1) PLANCK CONSTANT OVER 2 PI
Block (blk) Letterlike_Symbols
General Category (gc) Lowercase Letter
Script (sc) Common
Bidirectional Category (bc) Left To Right
Combining Class (ccc) Not Reordered
Decomposition Type (dt) Font
Decomposition Mapping (dm)
Lowercase (Lower)
Simple Lowercase Mapping (slc)
Lowercase Mapping (lc)
Uppercase (Upper)
Simple Uppercase Mapping (suc)
Uppercase Mapping (uc)
Simple Titlecase Mapping (stc)
Titlecase Mapping (tc)
Case Folding (cf)
ASCII Hex Digit (AHex)
Alphabetic (Alpha)
Bidi Control (Bidi_C)
Bidi Mirrored (Bidi_M)
Bidi Paired Bracket (bpb)
Bidi Paired Bracket Type (bpt) None
Cased (Cased)
Composition Exclusion (CE)
Case Ignorable (CI)
Full Composition Exclusion (Comp_Ex)
Changes When Casefolded (CWCF)
Changes When Casemapped (CWCM)
Changes When NFKC Casefolded (CWKCF)
Changes When Lowercased (CWL)
Changes When Titlecased (CWT)
Changes When Uppercased (CWU)
Dash (Dash)
Deprecated (Dep)
Default Ignorable Code Point (DI)
Diacritic (Dia)
East Asian Width (ea) Neutral
Extender (Ext)
FC NFKC Closure (FC_NFKC)
Grapheme Cluster Break (GCB) Any
Grapheme Base (Gr_Base)
Grapheme Extend (Gr_Ext)
Hex Digit (Hex)
Hangul Syllable Type (hst) Not Applicable
Hyphen (Hyphen)
ID Continue (IDC)
Ideographic (Ideo)
ID Start (IDS)
IDS Binary Operator (IDSB)
IDS Trinary Operator and (IDST)
InMC (InMC)
Indic Positional Category (InPC) NA
Indic Syllabic Category (InSC) Other
ISO 10646 Comment (isc)
Joining Group (jg) No_Joining_Group
Join Control (Join_C)
Jamo Short Name (JSN)
Joining Type (jt) Non Joining
Line Break (lb) Alphabetic
Logical Order Exception (LOE)
Math (Math)
Noncharacter Code Point (NChar)
NFC Quick Check (NFC_QC) Yes
NFD Quick Check (NFD_QC) Yes
NFKC Casefold (NFKC_CF)
NFKC Quick Check (NFKC_QC) No
NFKD Quick Check (NFKD_QC) No
Numeric Type (nt) None
Numeric Value (nv) NaN
Other Alphabetic (OAlpha)
Other Default Ignorable Code Point (ODI)
Other Grapheme Extend (OGr_Ext)
Other ID Continue (OIDC)
Other ID Start (OIDS)
Other Lowercase (OLower)
Other Math (OMath)
Other Uppercase (OUpper)
Pattern Syntax (Pat_Syn)
Pattern White Space (Pat_WS)
Quotation Mark (QMark)
Sentence Break (SB) Lower
Simple Case Folding (scf)
Script Extension (scx) Common
Soft Dotted (SD)
STerm (STerm)
Terminal Punctuation (Term)
Unified Ideograph (UIdeo)
Variation Selector (VS)
Word Break (WB) ALetter
White Space (WSpace)
XID Continue (XIDC)
XID Start (XIDS)
Expands On NFC (XO_NFC)
Expands On NFD (XO_NFD)
Expands On NFKC (XO_NFKC)
Expands On NFKD (XO_NFKD)