The quantum number n first appeared in the Bohr model where it determines the radius of each circular electron orbit.

Depiction of a hydrogen atom showing the diameter as about twice the Bohr model radius.

: is the Bohr radius,

The quantum mass of an electron, the Compton wavelength, can be determined through various forms of spectroscopy and is closely related to the Rydberg constant, the Bohr radius, and the classical electron radius.

Its Bohr radius and ionization energy are within 0. 5 % of hydrogen, deuterium, and tritium.

* The ratio of three characteristic lengths: the classical electron radius, the Bohr radius and the Compton wavelength of the electron:

* a < sub > 0 </ sub >, the accepted mathematical symbol for the Bohr radius

Solid metallic hydrogen is predicted to consist of a crystal lattice of hydrogen nuclei ( namely, protons ), with a spacing which is significantly smaller than the Bohr radius.

"< ref group = note > 2 < sup >− 64 </ sup > seconds is about 54 zeptoseconds ( light would travel 16. 26 picometres, or approximately 0. 31 × Bohr radius ), and 2 < sup > 64 </ sup > seconds is about 585 billion years .</ ref >

* Bohr radius, radius of atomic orbit in Bohr model

The Bohr radius is a physical constant, approximately equal to the most probable distance between the proton and electron in a hydrogen atom in its ground state.

The precise definition of the Bohr radius is:

Or, in Gaussian units the Bohr radius is simply

According to 2010 CODATA the Bohr radius has a value of 5. 2917721092 ( 17 ) m ( i. e., approximately 53 pm or 0. 53 angstroms ).

In the simplest atom, hydrogen, a single electron orbits the nucleus and its smallest possible orbit, with lowest energy, has an orbital radius almost equal to the Bohr radius.

( It is not exactly the Bohr radius due to the reduced mass effect.

Although the Bohr model is no longer in use, the Bohr radius remains very useful in atomic physics calculations, due in part to its simple relationship with other fundamental constants.

The Bohr model | Rutherford – Bohr model of the hydrogen atom.

File: Niels Bohr. jpg | Niels Bohr ( 1885-1962 ): used quantum mechanical model ( known as the Bohr model ) of the atom which theorized that electrons travel in discrete orbits around the nucleus, showed how electron energy levels are related to spectral lines, received the Nobel Prize in Physics in 1922.

From left to right: Top row-Archimedes, Aristotle, Alhazen | Ibn al-Haytham, Leonardo da Vinci, Galileo Galilei, Antonie van Leeuwenhoek ; Second row-Isaac Newton, James Hutton, Antoine Lavoisier, John Dalton, Charles Darwin, Gregor Mendel ; Third row-Louis Pasteur, James Clerk Maxwell, Henri Poincaré, Sigmund Freud, Nikola Tesla, Max Planck ; Fourth row-Ernest Rutherford, Marie Curie, Albert Einstein, Niels Bohr, Erwin Schrödinger, Enrico Fermi ; Bottom row-J. Robert Oppenheimer, Alan Turing, Richard Feynman, E. O. Wilson, Jane Goodall, Stephen Hawking

In the simplified Bohr model | Rutherford Bohr model of the hydrogen atom, the Balmer lines result from an electron jump between the second energy level closest to the nucleus, and those levels more distant.

Supercomputer simulation of the interference of two counter-circulating Bohr_atom | Bohr ( Trojan_wave_packet | Trojan ) electrons in hydrogen atom in electromagnetic field

When the size of the quantum dot is smaller than the critical characteristic length called the Exciton Bohr radius, the electrons crowding lead to the splitting of the original energy levels into smaller ones with smaller gaps between each successive level.

The horizontal axis is the radius, or the size, of the quantum dots and a < sub > b </ sub >* is the Exciton Bohr radius.

; Band gap energy: The band gap can become smaller in the strong confinement regime where the size of the quantum dot is smaller than the Exciton Bohr radius ( a < sub > b </ sub >* in the figure ) as the energy levels split up.

When the size of the semiconductor crystal is smaller than the Exciton Bohr radius, the Coulomb interaction must be modified to fit the situation.

* The atomic length scale is meters and is given by the size of hydrogen atom ( i. e., the Bohr radius ( approximately 53 pm )) which is set by the electron's Compton wavelength times the fine-structure constant:.

In insulators or semiconductors a collective screening cannot take place and the muon will usually pick-up one electron and form a so-called muonium ( Mu = μ < sup >+</ sup >+ e < sup >-</ sup >), which has similar size ( Bohr radius ), reduced-mass and ionization energy to the hydrogen atom.

Although the Bohr model of the hydrogen atom could be explained in this way, the spectrum of the helium atom ( classically an unsolvable 3-body problem ) could not be predicted.

Learning from these experiments, Danish physicist Niels Bohr proposed in 1913 that the electrons in atoms are arranged in shells surrounding the nucleus, and that for all noble gases except helium the outermost shell always contains eight electrons.

Moseley, after discussions with Bohr who was at the same lab ( and who had used Van den Broek's hypothesis in his Bohr model of the atom ), decided to test Van den Broek and Bohr's hypothesis directly, by seeing if spectral lines emitted from excited atoms fit the Bohr theory's demand that the frequency of the spectral lines be proportional to a measure of the square of Z.

Still, the Bohr model's use of quantized angular momenta and therefore quantized energy levels was a significant step towards the understanding of electrons in atoms, and also a significant step towards the development of quantum mechanics in suggesting that quantized restraints must account for all discontinuous energy levels and spectra in atoms.

In the early work of Max Planck, Albert Einstein and Niels Bohr, the existence of energy in discrete quantities had been postulated, in order to explain phenomena, such as the spectrum of black-body radiation, the photoelectric effect, and the stability and spectrum of atoms such as hydrogen, that had eluded explanation by, and even appeared to be in contradiction with, classical physics.

Dutch physicists Hendrik B. G. Casimir and Dirk Polder at Philips Research Labs proposed the existence of a force between two polarizable atoms and between such an atom and a conducting plate in 1947, and, after a conversation with Niels Bohr who suggested it had something to do with zero-point energy, Casimir alone formulated the theory predicting a force between neutral conducting plates in 1948 ; the former is called the Casimir-Polder force while the latter is the Casimir effect in the narrow sense.

In 1913, Niels Bohr showed that atoms could only emit discrete amounts of energy, thus explaining the discrete lines seen in emission and absorption spectra.

The Bohr model exhibits difficulty for atoms with atomic number greater than 137, for the speed of an electron in a 1s electron orbital, v, is given by

The Bohr model explains the atomic spectrum of hydrogen ( see hydrogen spectral series ) as well as various other atoms and ions.

By assuming blackbody radiation is quantized, Bohr showed that the atoms were also quantized, in the sense that they could only emit discrete amounts of energy.

The Bohr model exhibits difficulty for atoms with atomic number greater than 137, for the speed of an electron in a 1s electron orbital, v, is given by

The Bohr model exhibits difficulty for atoms with atomic number greater than 137, for the speed of an electron in a 1s electron orbital, v, is given by

When the Bohr treatment is extended to hydrogenic-like atoms using the Quantum Rule, the Bohr radius becomes

If the number of atoms making up the meter prototype remains unchanged ( as it should for a stable prototype ), then a perceived change in the value of c would be the consequence of the more fundamental change in the dimensionless ratio of the Planck length to the sizes of atoms or to the Bohr radius or, alternatively, as the dimensionless ratio of the Planck time to the period of a particular caesium-133 radiation or both.

where is the permeability constant, is the number of magnetic atoms ( or molecules ) per unit volume, is the Landé g-factor, ( 9. 27400915e-24 J / T or A · m < sup > 2 </ sup >) is the Bohr magneton, is the angular momentum quantum number and is Boltzmann's constant.

Following conversations in 1913 with Niels Bohr, a fellow worker in Ernest Rutherford's Cavendish laboratory, Moseley had become interested in the Bohr model of the atom, in which the spectra of light emitted by atoms is proportional to the square of Z, the charge on their nucleus ( which had just been discovered two years before ).

However, for hydrogenic atoms ( those in which the electron acts as though it circles a single structure with effective charge Z ), Bohr realized from his derivation that an extra quantity would need to be added to the conventional, in order to account for the extra pull on the electron, and thus the extra energy between levels, as a result of the increased nuclear charge.

Later, Niels Bohr showed that atoms could only emit discrete amounts of energy.

Neutron diffraction and other techniques have shown that a magnetic moment of around 3. 7 Bohr magnetons resides almost solely on the manganese atoms.