Share
VIDEOS 1 TO 50
Quantum Chemistry 9.1 - Atomic Units
Quantum Chemistry 9.1 - Atomic Units
Published: 2016/08/14
Channel: TMP Chem
In Depth: Atomic Mass Units | Chemistry for All | The Fuse School
In Depth: Atomic Mass Units | Chemistry for All | The Fuse School
Published: 2014/08/10
Channel: FuseSchool - Global Education
Atomic Mass Units
Atomic Mass Units
Published: 2010/05/26
Channel: ProfessorChemistry
Atomic Mass: Introduction
Atomic Mass: Introduction
Published: 2012/10/09
Channel: Tyler DeWitt
Quantum Chemistry 9.1 - Atomic Units (Old Version)
Quantum Chemistry 9.1 - Atomic Units (Old Version)
Published: 2014/02/19
Channel: TMP Chem
Atomic Mass Units In depth | The Chemistry Journey | The Fuse School
Atomic Mass Units In depth | The Chemistry Journey | The Fuse School
Published: 2013/09/09
Channel: FuseSchool - Global Education
Atomic units
Atomic units
Published: 2014/12/05
Channel: Audiopedia
UNM Phys 531 2011   Lec01   Introduction  Atomic Units, Hydrogen
UNM Phys 531 2011 Lec01 Introduction Atomic Units, Hydrogen
Published: 2016/04/19
Channel: CosmoLearning
Converting Between Moles, Atoms, and Molecules
Converting Between Moles, Atoms, and Molecules
Published: 2014/05/06
Channel: Tyler DeWitt
Atomic units
Atomic units
Published: 2016/01/22
Channel: WikiAudio
Convert Mass to Mass - Atomic Mass Units to Grams
Convert Mass to Mass - Atomic Mass Units to Grams
Published: 2013/02/03
Channel: Professor Heath's Chemistry Channel
Chem 131A. Lec 17. Quantum Principles: Approximation Methods: Variational Principle, Atomic Units
Chem 131A. Lec 17. Quantum Principles: Approximation Methods: Variational Principle, Atomic Units
Published: 2014/05/28
Channel: UCI Open
Chatoms = Chat Atoms : Atomic Units of Conversation
Chatoms = Chat Atoms : Atomic Units of Conversation
Published: 2012/03/28
Channel: Gant Laborde
Atomic weight and atomic mass | Atoms, compounds, and ions | Chemistry | Khan Academy
Atomic weight and atomic mass | Atoms, compounds, and ions | Chemistry | Khan Academy
Published: 2014/11/24
Channel: Khan Academy
1.4.3 Atomic Mass Unit
1.4.3 Atomic Mass Unit
Published: 2017/05/14
Channel: asan taleem
atomic mass units
atomic mass units
Published: 2012/09/29
Channel: stewartphysics
How to Calculate Atomic Mass Practice Problems
How to Calculate Atomic Mass Practice Problems
Published: 2012/10/05
Channel: Tyler DeWitt
Chatoms Atomic Units of Conversation!
Chatoms Atomic Units of Conversation!
Published: 2011/12/29
Channel: SuperJonesable
Atomic Mass
Atomic Mass
Published: 2010/09/03
Channel: Brightstorm
6. Atoms II
6. Atoms II
Published: 2015/03/23
Channel: MIT OpenCourseWare
P Chem Atomic Units, Nuclear Charge, Probability-7
P Chem Atomic Units, Nuclear Charge, Probability-7
Published: 2013/12/13
Channel: Mark J
7-2   Unified Atomic Mass Units
7-2 Unified Atomic Mass Units
Published: 2016/05/24
Channel: IBMathandPhysics
P Chem Hamiltonian in Atomic Units, Determinants, Variational Principle-8
P Chem Hamiltonian in Atomic Units, Determinants, Variational Principle-8
Published: 2013/12/13
Channel: Mark J
2.1 B Atomic Mass Units (amu)
2.1 B Atomic Mass Units (amu)
Published: 2011/11/26
Channel: Rebeca Zambrano
Stage 4 - The Atomic Unit
Stage 4 - The Atomic Unit
Published: 2016/11/16
Channel: Ananya Tummallapalli
Chemistry:  Average Atomic Mass (amu, Daltons, etc.) - 2 examples | Homework Tutor
Chemistry: Average Atomic Mass (amu, Daltons, etc.) - 2 examples | Homework Tutor
Published: 2014/03/04
Channel: Socratica
Atomic Mass Unit | Relative Atomic Mass | Relation between the two | How to Calculate RAM
Atomic Mass Unit | Relative Atomic Mass | Relation between the two | How to Calculate RAM
Published: 2013/10/13
Channel: Basics Of Chemistry
Atomic Unit
Atomic Unit
Published: 2012/07/01
Channel: dbld7241
Atomic Mass Unit, Atomic Mass
Atomic Mass Unit, Atomic Mass
Published: 2016/02/08
Channel: Richard Louie Chemistry Lectures
Atomic mass unit
Atomic mass unit
Published: 2014/08/06
Channel: Audiopedia
Atomic Mass
Atomic Mass
Published: 2014/01/16
Channel: G.D. Thomas
DomiNations - THE ATOMIC AGE is HERE !!! NEW UNITS & NEW WONDERS ! (Ep #39)
DomiNations - THE ATOMIC AGE is HERE !!! NEW UNITS & NEW WONDERS ! (Ep #39)
Published: 2016/11/08
Channel: TheGameHuntah Gaming
amu / Atomic Mass Unit || Unified Mass || Chemistry Tutor || chemistry concepts
amu / Atomic Mass Unit || Unified Mass || Chemistry Tutor || chemistry concepts
Published: 2017/04/07
Channel: the simple life channel
Relative atomic mass and Atomic mass unit in Urdu   Sabaq Foundation 26
Relative atomic mass and Atomic mass unit in Urdu Sabaq Foundation 26
Published: 2016/08/21
Channel: Learning Paradise
What
What's the Difference between Mass Number and Atomic Mass?
Published: 2012/10/03
Channel: Tyler DeWitt
Preparatory Chemistry Atomic Mass Units, Atomic Number, and Mass Number
Preparatory Chemistry Atomic Mass Units, Atomic Number, and Mass Number
Published: 2013/09/18
Channel: Pathways to Chemistry
Atomic Unit car club
Atomic Unit car club
Published: 2012/06/20
Channel: Allen Taylor
DomiNations - APC and ATTACK HELICOPTER ! NEW ATOMIC AGE UNITS ! (Ep #40)
DomiNations - APC and ATTACK HELICOPTER ! NEW ATOMIC AGE UNITS ! (Ep #40)
Published: 2016/11/09
Channel: TheGameHuntah Gaming
Atomic Unit 1
Atomic Unit 1
Published: 2012/07/01
Channel: dbld7241
Atomic Mass, Mass Number and Unified Atomic Mass Unit
Atomic Mass, Mass Number and Unified Atomic Mass Unit
Published: 2015/03/29
Channel: NinetyEast
Atomic energy council closes 3 x-ray units in Kampala clinics
Atomic energy council closes 3 x-ray units in Kampala clinics
Published: 2015/03/24
Channel: NTVUganda
Mass Conversions - Atomic Mass Units to Grams 001
Mass Conversions - Atomic Mass Units to Grams 001
Published: 2012/03/03
Channel: Professor Heath's Chemistry Channel
Atomic Mass Units
Atomic Mass Units
Published: 2012/07/09
Channel: Angles and Acid
28 - Nuclear Physics - Unified atomic mass unit
28 - Nuclear Physics - Unified atomic mass unit
Published: 2016/07/21
Channel: Pre-Med Academy
The Atomic Mass Unit
The Atomic Mass Unit
Published: 2017/05/29
Channel: Math & Physics
Atomic & Molecular Mass | Some basic concepts of chemistry | Chemistry | IIT JEE | Class 11 | C1.1.2
Atomic & Molecular Mass | Some basic concepts of chemistry | Chemistry | IIT JEE | Class 11 | C1.1.2
Published: 2016/07/25
Channel: Avanti Gurukul
HC10 Atomic Mass Units and Gram to Mole Conversions
HC10 Atomic Mass Units and Gram to Mole Conversions
Published: 2013/02/01
Channel: Tom Horsley
Dominations Update 5.0 || The Atomic Age || introduction by StabDominations | 2016.11.08
Dominations Update 5.0 || The Atomic Age || introduction by StabDominations | 2016.11.08
Published: 2016/11/08
Channel: StabDominations
Atomic Mass - Atom and Molecules  : CBSE Class 9  IX Science
Atomic Mass - Atom and Molecules : CBSE Class 9 IX Science
Published: 2014/09/02
Channel: Dronstudy.com
Christian Bök discusses units in language and art
Christian Bök discusses units in language and art
Published: 2010/06/17
Channel: pennsound
NEXT
GO TO RESULTS [51 .. 100]

WIKIPEDIA ARTICLE

From Wikipedia, the free encyclopedia
Jump to: navigation, search

Atomic units (au or a.u.) form a system of natural units which is especially convenient for atomic physics calculations. There are two different kinds of atomic units, Hartree atomic units[1] and Rydberg atomic units, which differ in the choice of the unit of mass and charge. This article deals with Hartree atomic units, where the numerical values of the following four fundamental physical constants are all unity by definition:

In Hartree units, the speed of light is approximately . Atomic units are often abbreviated "a.u." or "au", not to be confused with the same abbreviation used also for astronomical units, arbitrary units, and absorbance units in different contexts.

Use and notation[edit]

Atomic units, like SI units, have a unit of mass, a unit of length, and so on. However, the use and notation is somewhat different from SI.

Suppose a particle with a mass of m has 3.4 times the mass of electron. The value of m can be written in three ways:

  • "". This is the clearest notation (but least common), where the atomic unit is included explicitly as a symbol.[2]
  • "" ("a.u." means "expressed in atomic units"). This notation is ambiguous: Here, it means that the mass m is 3.4 times the atomic unit of mass. But if a length L were 3.4 times the atomic unit of length, the equation would look the same, "" The dimension needs to be inferred from context.[2]
  • "". This notation is similar to the previous one, and has the same dimensional ambiguity. It comes from formally setting the atomic units to 1, in this case , so .[3][4]

Fundamental atomic units[edit]

These four fundamental constants form the basis of the atomic units (see above). Therefore, their numerical values in the atomic units are unity by definition.

Fundamental atomic units
Dimension Name Symbol/Definition Value in SI units[5]
mass electron rest mass 9.10938291(40)×10−31 kg
charge elementary charge 1.602176565(35)×10−19 C
action reduced Planck's constant 1.054571726(47)×10−34 J·s
electric constant−1 Coulomb force constant 8.9875517873681×109 kg·m3·s−2·C−2

Related physical constants[edit]

Dimensionless physical constants retain their values in any system of units. Of particular importance is the fine-structure constant . This immediately gives the value of the speed of light, expressed in atomic units.

Some physical constants expressed in atomic units
Name Symbol/Definition Value in atomic units
speed of light
classical electron radius
proton mass

Derived atomic units[edit]

Below are given a few derived units. Some of them have proper names and symbols assigned, as indicated in the table. kB is the Boltzmann constant.

Derived atomic units
Dimension Name Symbol Expression Value in SI units Value in more common units
length bohr 5.2917721092(17)×10−11 m[6] 0.052917721092(17) nm = 0.52917721092(17) Å
energy hartree 4.35974417(75)×10−18 J 27.211385 eV = 627.509 kcal·mol−1
time 2.418884326505(16)×10−17 s
velocity 2.1876912633(73)×106 m·s−1
force 8.2387225(14)×10−8 N 82.387 nN = 51.421 eV·Å−1
temperature 3.1577464(55)×105 K
pressure 2.9421912(19)×1013 Pa
electric field 5.14220652(11)×1011 V·m−1 5.14220652(11) GV·cm−1 = 51.4220652(11) V·Å−1
electric potential 2.721138505(60)×101 V
electric dipole moment 8.47835326(19)×10−30 C·m 2.541746 D
Magnetic field (SI) 2.35×105 T 2.35×109 G
Magnetic dipole moment (SI) 2 (Bohr magneton)
Magnetic field (cgs) 1.72×103 T 1.72×107 G
Magnetic dipole moment (cgs)

SI and Gaussian-CGS variants, and magnetism-related units[edit]

There are two common variants of atomic units, one where they are used in conjunction with SI units for electromagnetism, and one where they are used with Gaussian-CGS units.[7] Although the units written above are the same either way (including the unit for electric field), the units related to magnetism are not. In the SI system, the atomic unit for magnetic field is

1 a.u. = = 2.35×105 T = 2.35×109 G,

and in the Gaussian-cgs unit system, the atomic unit for magnetic field is

1 a.u. = = 1.72×103 T = 1.72×107 G.

(These differ by a factor of α.)

Other magnetism-related quantities are also different in the two systems. An important example is the Bohr magneton: In SI-based atomic units,[8]

a.u.

and in Gaussian-based atomic units,[9]

a.u.

Bohr model in atomic units[edit]

Atomic units are chosen to reflect the properties of electrons in atoms. This is particularly clear from the classical Bohr model of the hydrogen atom in its ground state. The ground state electron orbiting the hydrogen nucleus has (in the classical Bohr model):

  • Orbital velocity = 1
  • Orbital radius = 1
  • Angular momentum = 1
  • Orbital period = 2π
  • Ionization energy = 12
  • Electric field (due to nucleus) = 1
  • Electrical attractive force (due to nucleus) = 1

Non-relativistic quantum mechanics in atomic units[edit]

The Schrödinger equation for an electron in SI units is

.

The same equation in au is

.

For the special case of the electron around a hydrogen atom, the Hamiltonian in SI units is:

,

while atomic units transform the preceding equation into

.

Comparison with Planck units[edit]

Both Planck units and au are derived from certain fundamental properties of the physical world, and are free of anthropocentric considerations. It should be kept in mind that au were designed for atomic-scale calculations in the present-day universe, while Planck units are more suitable for quantum gravity and early-universe cosmology. Both au and Planck units normalize the reduced Planck constant. Beyond this, Planck units normalize to 1 the two fundamental constants of general relativity and cosmology: the gravitational constant G and the speed of light in a vacuum, c. Atomic units, by contrast, normalize to 1 the mass and charge of the electron, and, as a result, the speed of light in atomic units is a large value, . The orbital velocity of an electron around a small atom is of the order of 1 in atomic units, so the discrepancy between the velocity units in the two systems reflects the fact that electrons orbit small atoms much slower than the speed of light (around 2 orders of magnitude slower).

There are much larger discrepancies in some other units. For example, the unit of mass in atomic units is the mass of an electron, while the unit of mass in Planck units is the Planck mass, a mass so large that if a single particle had that much mass it might collapse into a black hole. Indeed, the Planck unit of mass is 22 orders of magnitude larger than the au unit of mass. Similarly, there are many orders of magnitude separating the Planck units of energy and length from the corresponding atomic units.

See also[edit]

Notes and references[edit]

  1. ^ Hartree, D. R. (1928). "The Wave Mechanics of an Atom with a Non-Coulomb Central Field. Part I. Theory and Methods". Mathematical Proceedings of the Cambridge Philosophical Society. 24 (1). Cambridge University Press. pp. 89–110. Bibcode:1928PCPS...24...89H. doi:10.1017/S0305004100011919. 
  2. ^ a b Pilar, Frank L. (2001). Elementary Quantum Chemistry. Dover Publications. p. 155. ISBN 978-0-486-41464-5. 
  3. ^ Bishop, David M. (1993). Group Theory and Chemistry. Dover Publications. p. 217. ISBN 978-0-486-67355-4. 
  4. ^ Drake, Gordon W. F. (2006). Springer Handbook of Atomic, Molecular, and Optical Physics (2nd ed.). Springer. p. 5. ISBN 978-0-387-20802-2. 
  5. ^ "The NIST Reference on Constants, Units and Uncertainty". National Institute of Standard and Technology. Retrieved 1 April 2012. 
  6. ^ "The NIST Reference on Constants, Units and Uncertainty". National Institute of Standard and Technology. Retrieved 21 January 2014. 
  7. ^ "A note on Units" (PDF). Physics 7550 — Atomic and Molecular Spectra. University of Colorado lecture notes. 
  8. ^ Chis, Vasile. "Atomic Units; Molecular Hamiltonian; Born-Oppenheimer Approximation" (PDF). Molecular Structure and Properties Calculations. Babes-Bolyai University lecture notes. 
  9. ^ Budker, Dmitry; Kimball, Derek F.; DeMille, David P. (2004). Atomic Physics: An Exploration through Problems and Solutions. Oxford University Press. p. 380. ISBN 978-0-19-850950-9. 

External links[edit]

Disclaimer

None of the audio/visual content is hosted on this site. All media is embedded from other sites such as GoogleVideo, Wikipedia, YouTube etc. Therefore, this site has no control over the copyright issues of the streaming media.

All issues concerning copyright violations should be aimed at the sites hosting the material. This site does not host any of the streaming media and the owner has not uploaded any of the material to the video hosting servers. Anyone can find the same content on Google Video or YouTube by themselves.

The owner of this site cannot know which documentaries are in public domain, which has been uploaded to e.g. YouTube by the owner and which has been uploaded without permission. The copyright owner must contact the source if he wants his material off the Internet completely.

Powered by YouTube
Wikipedia content is licensed under the GFDL and (CC) license