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From Wikipedia

Bohr model

In atomic physics, the Bohr model, devised by Niels Bohr, depicts the atom as a small, positively charged nucleus surrounded by electrons that travel in circular orbits around the nucleus—similar in structure to the solar system, but with electrostatic forces providing attraction, rather than gravity. This was an improvement on the earlier cubic model (1902), the plum-pudding model (1904), the Saturnian model (1904), and the Rutherford model (1911). Since the Bohr model is a quantum physics-based modification of the Rutherford model, many sources combine the two, referring to the Rutherford–Bohr model.

Introduced by Niels Bohr in 1913, the model's key success lay in explaining the Rydberg formula for the spectral emission lines of atomic hydrogen. While the Rydberg formula had been known experimentally, it did not gain a theoretical underpinning until the Bohr model was introduced. Not only did the Bohr model explain the reason for the structure of the Rydberg formula, it also provided a justification for its empirical results in terms of fundamental physical constants.

The Bohr model is a primitive model of the hydrogen atom. As a theory, it can be derived as a first-order approximation of the hydrogen atom using the broader and much more accurate quantum mechanics, and thus may be considered to be an obsolete scientific theory. However, because of its simplicity, and its correct results for selected systems (see below for application), the Bohr model is still commonly taught to introduce students to quantum mechanics, before moving on to the more accurate but more complex valence shell atom. A related model was originally proposed by Arthur Erich Haas in 1910, but was rejected. The quantum theory of the period between Planck's discovery of the quantum (1900) and the advent of a full-blown quantum mechanics (1925) is often referred to as the old quantum theory.


In the early 20th century, experiments by Ernest Rutherford established that atoms consisted of a diffuse cloud of negatively charged electrons surrounding a small, dense, positively charged nucleus. Given this experimental data, Rutherford naturally considered a planetary-model atom, the Rutherford model of 1911 – electrons orbiting a solar nucleus – however, said planetary-model atom has a technical difficulty. The laws of classical mechanics (i.e. the Larmor formula), predict that the electron will release electromagnetic radiation while orbiting a nucleus. Because the electron would lose energy, it would gradually spiral inwards, collapsing into the nucleus. This atom model is disastrous, because it predicts that all atoms are unstable.

Also, as the electron spirals inward, the emission would gradually increase in frequency as the orbit got smaller and faster. This would produce a continuous smear, in frequency, of electromagnetic radiation. However, late 19th century experiments with electric discharges through various low-pressure gases in evacuated glass tubes had shown that atoms will only emit light (that is, electromagnetic radiation) at certain discrete frequencies.

To overcome this difficulty, Niels Bohr proposed, in 1913, what is now called the Bohr model of the atom. He suggested that electrons could only have certain classical motions:

  1. The electrons can only travel in special orbits: at a certain discrete set of distances from the nucleus with specific energies.
  2. The electrons of an atom revolve around the nucleus in orbits. These orbits are associated with definite energies and are also called energy shells or energy levels. Thus, the electrons do not continuously lose energy as they travel in a particular orbit. They can only gain and lose energy by jumping from one allowed orbit to another, absorbing or emitting electromagnetic radiation with a frequency ν determined by the energy difference of the levels according to the Planck relation:\Delta{E} = E_2-E_1=h\nu \ , where h is Planck's constant.
  3. The frequency of the radiation emitted at an orbit of period T is as it would be in classical mechanics; it is the reciprocal of the classical orbit period: \nu = {1\over T}

The significance of the Bohr model is that the laws of classical mechanics apply to the motion of the electron about the nucleus only when restricted by a quantum rule. Although rule 3 is not completely well defined for small orbits, because the emission process involves two orbits with two different periods, Bohr could determine the energy spacing between levels using rule 3 and come to an exactly correct quantum rule: the angular momentum L is restricted to be an integer multiple of a fixed unit:

L = n{h \over 2\pi} = n\hbar

where n = 1, 2, 3, ... is called the principal quantum number, and ħ = h/2Ï€. The lowest value of n is 1; this gives a smallest possible orbital radius of 0.0529 nm known as the Bohr radius. Once an electron is in this lowest orbit, it can get no closer to the proton. Starting from the angular momentum quantum rule Bohr was a

3D modeling

In 3D computer graphics, 3D modeling (also known as meshing) is the process of developing a mathematical representation of any three-dimensionalsurface of object (either inanimate or living) via specialized software. The product is called a 3D model. It can be displayed as a two-dimensional image through a process called 3D renderingor used in acomputersimulation of physical phenomena. The model can also be physically created using 3D Printing devices.

Models may be created automatically or manually. The manual modeling process of preparing geometric data for 3D computer graphics is similar to plastic arts such as sculpting.


3D models represent a 3D object using a collection of points in 3D space, connected by various geometric entities such as triangles, lines, curved surfaces, etc. Being a collection of data (points and other information), 3D models can be created by hand, algorithmically (procedural modeling), or scanned.

3D models are widely used anywhere in 3D graphics. Actually, their use predates the widespread use of 3D graphics on personal computers. Many computer games used pre-rendered images of 3D models as sprites before computers could render them in real-time.

Today, 3D models are used in a wide variety of fields. The medical industry uses detailed models of organs. The movie industry uses them as characters and objects for animated and real-life motion pictures. The video game industry uses them as assets for computer and video games. The science sector uses them as highly detailed models of chemical compounds. The architecture industry uses them to demonstrate proposed buildings and landscapes through Software Architectural Models. The engineering community uses them as designs of new devices, vehicles and structures as well as a host of other uses. In recent decades the earth science community has started to construct 3D geological models as a standard practice.


Almost all 3D models can be divided into two categories.

  • Solid - These models define the volume of the object they represent (like a rock). These are more realistic, but more difficult to build. Solid models are mostly used for nonvisual simulations such as medical and engineering simulations, for CAD and specialized visual applications such as ray tracing and constructive solid geometry
  • Shell/boundary - these models represent the surface, e.g. the boundary of the object, not its volume (like an infinitesimally thin eggshell). These are easier to work with than solid models. Almost all visual models used in games and film are shell models.

Because the appearance of an object depends largely on the exterior of the object, boundary representations are common in computer graphics. Two dimensional surfaces are a good analogy for the objects used in graphics, though quite often these objects are non-manifold. Since surfaces are not finite, a discrete digital approximation is required: polygonal meshes (and to a lesser extent subdivision surfaces) are by far the most common representation, although point-based representations have been gaining some popularity in recent years. Level sets are a useful representation for deforming surfaces which undergo many topological changes such as fluids.

The process of transforming representations of objects, such as the middle point coordinate of a sphere and a point on its circumference into a polygon representation of a sphere, is called tessellation. This step is used in polygon-based rendering, where objects are broken down from abstract representations ("primitives") such as spheres, cones etc., to so-called meshes, which are nets of interconnected triangles. Meshes of triangles (instead of e.g. squares) are popular as they have proven to be easy to render using scanline rendering. Polygon representations are not used in all rendering techniques, and in these cases the tessellation step is not included in the transition from abstract representation to rendered scene.

Modeling processes

There are five popular ways to represent a model:

  • Polygonal modeling - Points in 3D space, called vertices, are connected by line segments to form a polygonal mesh. Used, for example, by Blender. The vast majority of 3D models today are built as textured polygonal models, because they are flexible and because computers can render them so quickly. However, polygons are planar and can only approximate curved surfaces using many polygons.
  • NURBS modeling - NURBS Surfaces are defined by spline curves, which are influenced by weighted control points. The curve follows (but does not necessarily interpolate) the points. Increasing the weight for a po

From Yahoo Answers

Question:I need to make a 3D Bohr's model. I want some suggestions for materials to use. Thank You

Answers:I'd use something like styrofoam or paper mache. They are cheap and easy to paint so you could easily label the different parts of the model.

Question:for science we have to make a 3-D Bohr model.i picked Beryllium(Be4) -supplies and directions would help *thanks*

Answers:I would like to help, but I also don't know. Sorry, friend.

Question:http://physics.uoregon.edu/~jimbrau/BrauImNew/Chap04/FG04_11.jpg the second picture is that of carbon....i have to make a 3d project for science class is that the right model to follow after if not please give me ideas yeah i have to use pipecleaners and styrophome balls i sont think that picture is gonna worl

Answers:yeah that would be the right model to use. http://www.mbe.doe.gov/me70/manhattan/images/AtomLabeledLarge.gif is one thats more familiar. Are you going to do the styrofoam ball and pipecleaner route or otherwise?

Question:Bohr Model, Atoms, Nucleus, Electrons, and Protons.

Answers:I would use painted styrofoam balls for the neutrons, protons, and electrons and wire to represent the orbitals. You can paint each particle a different color and glue the nucleus together and use the wire to put the elctrons in the orbitals. You should be able to get this stuff at any craft store or a walmart that has a craft section.

From Youtube

3D Bohr Model of a Sodium-26 Isotope Atom :This is a 3D Bohr model of a sodium-26 isotope atom. The red particles represent protons, the blue are neutrons, and the yellow particles orbiting the nucleus are electrons. The electron shells are 2-8-1. I created this in the Maya 2009 software.

Bohr :Bohr model