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Topic: Bohr radius

	Bohr model - Wikipedia, the free encyclopedia
		Because of its simplicity, the Bohr model is still commonly taught to introduce students to quantum mechanics.
		The Bohr model is actually only accurate for one-electron systems such as the hydrogen atom or singly-ionized helium.
		Bohr did not make this assumption (known as the de Broglie hypothesis) in his original derivation, because it hadn't been proposed at the time.
	en.wikipedia.org /wiki/Bohr_model (928 words)

	Bohr radius - Wikipedia, the free encyclopedia
		In the Bohr model of the structure of an atom, put forward by Niels Bohr in 1913, electrons orbit a central nucleus.
		The Bohr radius is often used as a unit in atomic physics, see atomic units.
		Note that the definition of Bohr radius does not include the effect of reduced mass, and so it is not precisely equal to the orbital radius of the electron in a hydrogen atom in the more physical model where reduced mass is included.
	en.wikipedia.org /wiki/Bohr_radius (255 words)

	Title
		Bohr asserted that this radiation consists of Einstein's photons, with frequency determined by their energy accourding to E = hf.
		Bohr argued that this means the atom's own energy must be restricted to discrete "levels" and that the photon emitted when the atom moves from a higher level to a lower one will have energy E
		Bohr assumed that hydrogen consists of a single electron orbiting a nucleus with a large mass and charge +e.
	www.phy.duke.edu /courses/100/lectures/Quan2/Qu2.html (1552 words)

	bohr (Site not responding. Last check: 2007-11-07)
		Bohr returned to Copenhagen during 1912 and continued to develop his new theory of the atom completing the work in 1913.
		Bohr is best known for the investigations of atomic structure referred to above and also for work on radiation, which won him the 1922 Nobel Prize for physics.
		Bohr's other major contributions, in addition to quantum theory, include his theoretical description of the periodic table of elements around 1920, his theory of the atomic nucleus being a compound structure in 1936, and his understanding of uranium fission in terms of the isotope 235 in 1939.
	indykfi.atomki.hu /indyKFI/MT/bohr.htm (951 words)

	eeCHEM Pressure Quiz (Site not responding. Last check: 2007-11-07)
		The radius of a hydrogen atom with n = 7 is
		The Bohr radius of hydrogen in the ground state is 52.9pm.
		The radius of a Bohr orbit in terms of the quantum number n and the nuclear charge Z is proportional to
	home.att.net /~eechem/pquiz/pq6.htm (390 words)

	Overview of Quantum Chemistry
		The important terms in these equations are the radius of the electron from the nucleus and the constant known as the
		Bohr radius, a value of 0.529 angstroms, or 0.528 Å.
		I used a Bohr radius of 52.9 picometers, with the electron radius increasing by increments of 2 pm.
	www.shodor.org /chemviz/overview/quantum.html (573 words)

	The Bohr Atom
		Bohr concluded that in an atom in its natural rest state, the electron must be in a special orbit, he called it a "stationary state" to which the usual rules of electromagnetic radiation didn't apply.
		Bohr suggested in a note to Rutherford in the summer of 1912 that requiring this energy be some constant (assumed to be of order of magnitude one) multiplied by hf would fix the size of the atom.
		Therefore, Bohr concluded K is fixed by requiring that the frequency of radiation emitted by a really large atom be correctly given by ordinary common sense -- that is, the frequency of the radiation must be the same as the orbital frequency of the electron, the number of cycles a second.
	galileo.phys.virginia.edu /classes/252/Bohr_Atom/Bohr_Atom.html (2892 words)

	Lengths
		The Bohr radius r is the approximate size of a hydrogen atom in its ground state.
		To complete this shoddy "derivation" of Bohr's radius, note that Delta v is probably about equal to the velocity of a classical electron going around a proton in an orbit the size of the Bohr radius.
		In other words, the classical electron radius is the radius the electron would have to have for all of its mass to be due to the electric field it produced, assuming it was a charged shell.
	math.ucr.edu /home/baez/lengths.html (2893 words)

	de Broglie Wave and Bohr Radius (Site not responding. Last check: 2007-11-07)
		According to Bohr, for a stable orbit, exactly one wavelength must fit on the path of the orbit.
		Your question, though, is a very good one, since the electron in the lowest Bohr orbit is not really a tiny planet circling a sun-like proton.
		The path length for the orbit = 2 * Pi * Bohr radius.
	www.newton.dep.anl.gov /askasci/phy00/phy00634.htm (220 words)

	[No title]
		The average Bohr radius for an electron (in the ground state) of an atom is ao/Z, where ao is the Bohr radius for hydrogen (ao=5.29 x10-11 m) and Z is the atomic number.
		The average atomic radius for a carbon atom is roughly 1.5x10-10 m.
		Determine the ratio of atomic radius to nuclear radius.
	spot.pcc.edu /~azable/ph203/Ph203_CH31_worksheet.doc (549 words)

	No Title (Site not responding. Last check: 2007-11-07)
		hence the radius of the orbit is quantized indeed.
		According to Bohr, electrons move in circular orbits, characterized by a quantum number n (which is a positive integer).
		Hence Bohr's model of the atom was succesful in explaining the energy levels in hydrogen.
	www.physics.orst.edu /~henri/Ph314/lect14/lecture_14.html (876 words)

	Bohr radius -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-07)
		The model says that the electrons orbit only at certain distances from the nucleus, depending on their energy.
		The Bohr radius () is the radius of the lowest energy orbit in the hydrogen atom:
		The Bohr radius is often used as a unit in atomic physics, typically in perturbative expansions of (Click link for more info and facts about wave function) wave function solutions.
	www.absoluteastronomy.com /encyclopedia/B/Bo/Bohr_radius.htm (203 words)

	Overview of Computational Chemistry
		Bohr, a scientist, was trying to understand why atoms do not collapse, as well as understand the various aspects of experimental spectra and the nature of light.
		Using Rydberg's equation which described the frequencies in a spectrum, Bohr was looking to understand atomic structure using the principles of classical theories of physics.
		For the first orbit where n=1, the radius r is called the Bohr radius, and is symbolized as a
	www.shodor.org /chemviz/overview/bohradius.html (203 words)

	Bohr radius - a Whatis.com definition (Site not responding. Last check: 2007-11-07)
		The Bohr radius is based on the so-called Bohr model of the atom, named after the Danish physicist and philosopher Niels Bohr (1884-1962).
		Bohr envisioned atoms as consisting of small, dense nuclei with positive electric charge, around which negatively charged electrons orbit in circular paths.
		However, the Bohr radius is still a useful constant because, in a sense, it represents the smallest mean radius normally attainable by a neutral atom.
	whatis.techtarget.com /gDefinition/0,294236,sid44_gci838634,00.html (186 words)

	The Bohr Model of the Atom
		Bohr leaves Manchester right after writing the memo and goes to Copenhagen and is married on August 1, 1912.
		Bohr argued that Planck's constant should be used to help account for the stability of the atom.
		Bohr also realized that, if he was correct, his theory should produce a constant with the units of length.
	dbhs.wvusd.k12.ca.us /webdocs/Electrons/Bohr-Model-part1.html (1361 words)

	Natural Length Contraction Mechanism Due to Kinetic Energy
		The change of Bohr radius is the fundamental cause of dilation of matter when atoms acquire kinetic energy.
		The Bohr radii of all the corresponding quantum states are shifted to a larger radius.
		When calculating the Bohr radius, the same mathematical relationship does not mean the same absolute energy.
	www.newtonphysics.on.ca /kinetic/length.html (5912 words)

	Bohr model (Site not responding. Last check: 2007-11-07)
		[[Image Link]] Bohr Model is a physical model that depicts the atom as a small positively charged nucleus with electrons in orbit at different levels, similar in structure to the solar system.
		Because of its simplicity, the Bohr model is still commonly used and taught today.
		In the early part of the 20th century, experiments by Ernest Rutherford and others had established that atoms consisted of a small dense positively charged nucleus surrounded by orbiting negatively charged electrons.
	www.sciencedaily.com /encyclopedia/bohr_model_1 (883 words)

	radius concept from the Astronomy knowledge base (Site not responding. Last check: 2007-11-07)
		This criterion was developed by Holmberg in 1958 to estimate the actual dimensions of the major and minor axes of a galaxy without regard to its orientation in space.
		Larmor radius (2 facts) - The radius of the circular orbit that a charged particle describes transverse to a magnetic field.
		velocity-of-light radius (2 facts) - The radius of a rotating neutron star at which the rotational velocity of the plasma approaches the velocity of light.
	www.csi.uottawa.ca:4321 /astronomy/radius.html (189 words)

	Electromagnetic Waves
		In this way the hydrogen atom is stable since the electron in the n=1 orbit does not have a lower orbit to go to and it does not radiate in the n=1 state, only when changing orbits.
		Moreover, the frequencies predicted by the Bohr formula were in excellent agreement with the experimentally observed frequencies.
		Thus Bohr was able to quantitatively explain the structure of atoms and give their size, even if his theory was a bit ad hoc.
	www-personal.umich.edu /~pberman/20bohr.html (671 words)

	Natural Length Contraction Due to Gravity
		Consequently, since the Bohr radius is increasing during the free fall, and the behavior of matter depends on the parameters existing at the location and at the velocity matter is traveling, this is the fundamental mechanism which explains exactly the advance of the perihelion of Mercury in its elliptical orbit.
		These considerations show the difference of the final atom structure (larger versus smaller Bohr radius) between an increase of potential energy, which does not possess any momentum and the increase of kinetic energy, which increases the size of the electron orbit.
		This explains the increase of Bohr radius due to the kinetic energy and the decrease of Bohr radius due to the gravitational energy as calculated in this paper.
	www.intalek.com /Index/Projects/Research/NaturalLengthContractionDueToGravity.htm (7904 words)

	Internal Relativistic Phenomena inside Atoms
		In order to be compatible with the Bohr equation and quantum mechanics, the length of the circumference of the orbit of an electron around a proton must be equal to an integer number of the wavelength of the electron.
		This satisfies the wave condition of the constructive interference of the electron wave after each translation since the radius of the orbit (therefore its circumference) of the moving atom is twice as large as the radius for the atom at rest as illustrated on figure 11.1.
		Consequently, the radius of the orbit changes because it is necessary to have an integer number of wavelengths in a circumference.
	www.newtonphysics.on.ca /EINSTEIN/Chapter11.html (2697 words)

	Structure of the Atom and the Periodic Law (Site not responding. Last check: 2007-11-07)
		Niels Bohr pointed out that a charged particle moving like the electron in an orbit would, according to the laws of electromagnetics, emit energy in the form of electromagnetic radiation.
		Bohr used the new theories of Max Planck to modify the Rutherford model.
		Bohr was able to show that the allowed transitions in a Bohr model hydrogen atom matched exactly the known spectrum of hydrogen.
	v.d.singleton.home.att.net /genchem/atom.htm (3719 words)

	Physics Help and Math Help - Physics Forums - The Bohr Model
		Bohr postulated that electrons in atoms can only move around a nucleus in certain circular orbits which are stable without radiating energy.
		The big step for Bohr was to suggest that they wont radiate energy as they circle the nucleus, this is a big departure from classical electromagnetic theory (as said).
		Also keep in mind that the Bohr-radius is calculated as that radius at which the probability of findinf the electron in its ground state is maximal...
	www.physicsforums.com /printthread.php?t=53956&pp=40 (5142 words)

	Hydrogen Ground State Properties (Site not responding. Last check: 2007-11-07)
		The Schrodinger equation confirms the first Bohr radius as the most probable radius but goes further to describe in detail the profile of probability for the electron radius.
		The average or "expectation value" of the radius for the electron in the ground state of hydrogen is obtained from the integral
		It may seem a bit surprising that the average value of r is 1.5 x the first Bohr radius, which is the most probable value.
	hyperphysics.phy-astr.gsu.edu /hbase/quantum/hydr.html (182 words)

	Relativity: Time, Length, Mass dilation; Energy and Momentum
		The radical step that Bohr took to find the radius of the orbit was to assume that the angular momentum cannot be any arbitrary value, but has to be discrete or quantized value.
		Usually we define the radius of the inner orbit as the Bohr radius, a
		Figure 2 shows the relation between the radius and the energy for the electron in the hydrogen atom.
	www.missioncollege.org /depts/physics/P4poe/P4D/DualityMatter.htm (1104 words)

	Chapter 7
		The Bohr Model: Bohr derived the energy levels of the hydrogen and hydrogen-like ions (i.e.
		However, the radius is not fixed but but is given by a probability distribution.
		The most probable radius is similar in magnitude to the value from the Bohr model.
	faculty.washington.edu /goutermn/chem142/overheads/overhd7.html (306 words)

	Online Unit Conversion - Convert from cable [U.S.] to bohr
		The Bohr is a unit of distance commonly used in particle physics.
		It was named after the Danish physicist Niels Bohr (1885-1962), who explained the structure of atoms in a famous paper in 1913.
		The Bohr radius represents the mean distance between the proton and the electron in an unexcited hydrogen atom.
	www.onlineunitconversion.com /cable.U.S_to_bohr.html (143 words)

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