Bohr Atom

Bohr Atomic Model :

The Bohr model of the atom is often called the planetary model.As shown in Figure 1 for a hydrogen atom, the Bohr model envisions the nucleus of the atom occupying a fixed position at the center of an atomic system with the electron revolving around the nucleus in the same way that a planet revolves around the sun. Niels Bohr was born on October 7, 1885, in Copenhagen, Denmark, to mother Ellen Adler, who was part of a successful Jewish banking clan, and father Christian Bohr, a celebrated physiology academic. The Bohr model shows the atom as a small, positively charged nucleus surrounded by orbiting electrons. Bohr was the first to discover that electrons travel in separate orbits around the nucleus.

The Bohr model of the atom, a radical departure from earlier, classical descriptions, was the first that incorporated quantum theory and was the predecessor of wholly quantum-mechanical models. The Bohr model and all of its successors describe the properties of atomic electrons in terms of a set of allowed (possible) values. Published February 16, 2008. Share Tweet Email. Nedsferatu writes, “I studied nanotechnology in school and got my enormous bohr atom during that time.”.

In 1913 Bohr proposed his quantized shell model of the atom to explain howelectrons can have stable orbits around the nucleus. The motion of theelectrons in the Rutherford model was unstable because, according toclassical mechanics and electromagnetic theory, any charged particlemoving on a curved path emits electromagnetic radiation; thus, theelectrons would lose energy and spiral into the nucleus. To remedy thestability problem, Bohr modified the Rutherford model by requiring thatthe electrons move in orbits of fixed size and energy. The energy of anelectron depends on the size of the orbit and is lower for smaller orbits.Radiation can occur only when the electron jumps from one orbit toanother. The atom will be completely stable in the state with the smallestorbit, since there is no orbit of lower energy into which the electron canjump.

Bohr's starting point was to realize that classical mechanics by itselfcould never explain the atom's stability. A stable atom has a certain sizeso that any equation describing it must contain some fundamental constantor combination of constants with a dimension of length. The classicalfundamental constants--namely, the charges and the masses of the electronand the nucleus--cannot be combined to make a length. Bohr noticed,however, that the quantum constant formulated by the German physicist MaxPlanck has dimensions which, when combined with the mass and charge of theelectron, produce a measure of length. Numerically, the measure is closeto the known size of atoms. This encouraged Bohr to use Planck's constantin searching for a theory of the atom.

Planck had introduced his constant in 1900 in a formula explaining thelight radiation emitted from heated bodies. According to classical theory,comparable amounts of light energy should be produced at all frequencies.This is not only contrary to observation but also implies the absurdresult that the total energy radiated by a heated body should be infinite.Planck postulated that energy can only be emitted or absorbed in discreteamounts, which he called quanta (the Latin word for 'how much'). Theenergy quantum is related to the frequency of the light by a newfundamental constant, h. When a body is heated, its radiant energy in aparticular frequency range is, according to classical theory, proportionalto the temperature of the body. With Planck's hypothesis, however, theradiation can occur only in quantum amounts of energy. If the radiantenergy is less than the quantum of energy, the amount of light in thatfrequency range will be reduced. Planck's formula correctly describesradiation from heated bodies. Planck's constant has the dimensions ofaction, which may be expressed as units of energy multiplied by time,units of momentum multiplied by length, or units of angular momentum. Forexample, Planck's constant can be written as h = 6.6x10-34 jouleseconds.

Using Planck's constant, Bohr obtained an accurate formula for the energylevels of the hydrogen atom. He postulated that the angular momentum ofthe electron is quantized--i.e., it can have only discrete values. Heassumed that otherwise electrons obey the laws of classical mechanics bytraveling around the nucleus in circular orbits. Because of thequantization, the electron orbits have fixed sizes and energies. Theorbits are labeled by an integer, the quantum number n.

With his model, Bohr explained how electrons could jump from one orbit toanother only by emitting or absorbing energy in fixed quanta. For example,if an electron jumps one orbit closer to the nucleus, it must emit energyequal to the difference of the energies of the two orbits. Conversely,when the electron jumps to a larger orbit, it must absorb a quantum oflight equal in energy to the difference in orbits.

Excerpt from the Encyclopedia Britannica without permission.

Bohr created the first model that accounted for the emission of specific frequencies of light from an excited hydrogen atom.

The Bohr model is derived using three statements.

(1) The energy of the electron in a hydrogen atom is the sum of the KE and the PE. The magnitude of the kinetic energy is determined by the movement of the electron. The potential energy results from the attraction between the electron and the proton.
Bohr atomic model picture

(1)

(m = mass of electron, v = velocity of the electron,

Z = # of protons, e = charge of an electron, r = radius)

(2) The force that keeps the electron in its orbit

is generated by the attraction of the electron for the nucleus.

Wordpress 4.9. So,

(2)

(3) Since experimentation reveals that the energy of an electron in a hydrogen atom must be quantized, Bohr postulated that the angular momentum (mvr) of the electron must be quantized.

(3)

(n is a counting number)

Bohr Atom Date

So, rearranging equation (3) gives

Bohr Atom Icon

Substituting for r in equation (2) and solving for v gives

Substituting for v and r in equation (1) gives

Substituting for v again gives

This simplifies to

The Bohr equation is in agreement with the Rhydberg equation, which is written below.

RH is the Rydberg constant, 2.18 x 10-18 J.

E1 = -2.18 x 10-18 J, E2 = -5.45 x 10-19 J, E3 = -2.42 x 10-19 J, = 0.

What is the energy and wavelength of the photon released when an electron moves from quantum level 3 to quantum level 2?

E = (-2.18 x 10-18) (1/22 - 1/32 )
Bohr atom oxygen
E = (-2.18 x 10-18) (0.139)
E = -3.03 x 10-19 J
(the negative sign tells us that energy is released)

Periodic Table Bohr

The energy that is released is released as a photon. From the photon's point of view the photon is gaining energy (the photon is being created).

Ephoton = hu

Ephoton = h(c/l)

3.03 x 10-19 J = (6.626 x 10-34 J s)(2.9979 x 108 m s-1)/l

l = 6.56 x 10-7 m

Bohr Atomic Models Worksheet Answers

l = 656 nm (red)

Bohr Atomic Model

Although the Bohr atom correctly accounts for hydrogen line spectrum, the model can not be extended to other atoms. Treating an electron as a particle fails to produce a model which can describe all the elements.

Bohr Atomic Theory For Kids