In 1913, Niels Bohr proposed a theory for the hydrogen atom, based on quantum theory that some physical quantities only take discrete values. Electrons move around a nucleus, but only in prescribed orbits, and If electrons jump to a lower-energy orbit, the difference is sent out as radiation. In 1913 Bohr proposed his quantized shell model of the atom to explain how electrons can have stable orbits around the nucleus. The motion of the electrons in the Rutherford model was unstable because, according to classical mechanics and electromagnetic theory, any charged particle. The Bohr Model has an atom consisting of a small, positively charged nucleus orbited by negatively charged electrons. Here's a closer look at the Bohr Model, which is sometimes called the Rutherford-Bohr Model. Overview of the Bohr Model Niels Bohr proposed the Bohr Model of the Atom in 1915.

1. Bohr Atom Theory
2. Bohr Atomic Model
3. Bohr Atomic Theory
4. Bohr Atomic Model Worksheet
5. Bohr Atomic Theory For Kids

The Bohr Atom

We often picture atoms as a miniature Solar System, with electrons orbiting around the central nucleus of protons and neutrons. This picture was first proposed in 1911 by the English physicist Ernest Rutherford, but it suffered from a major theoretical problem. When an object moves along a curved path, such as an electron does in orbit around the nucleus, it experiences an acceleration. (Recall that if an object moves along anynon-straight line it experiences an acceleration). The difficulty this posses is that experiment and theory both show that a charge radiates when it accelerates and that the radiation carries energy away from the particle. Thus, an orbiting electron should gradually lose energy and spiral into the nucleus.

In 1912, the Danish physicist Neils Bohr proposed a solution to this . His solution had three special parts.

The Bohr radius (a 0) is a physical constant, equal to the most probable distance between the nucleus and the electron in a hydrogen atom in its ground state (non-relativistic and with an infinitely heavy proton). It is named after Niels Bohr, due to its role in the Bohr model of an atom. Its value is 5.291 772 109 03 (80) × 10 −11 m. Bohr’s model of the hydrogen atom, proposed by Niels Bohr in 1913, was the first quantum model that correctly explained the hydrogen emission spectrum. Bohr’s model combines the classical mechanics of planetary motion with the quantum concept of photons.

• First, electron orbits are quantized (as we discussed in chapter 3.). That is an electron can not orbit at any arbitrary distance from the nucleus, but at only certain prescribed distances.
• Second, when an electron moves in such an orbit, the laws of classical radiation do not apply and the electron does not radiate.
• Third, an atom emits light only when an electron drops from an upper to a lower orbit.

Bohr then went on from these assumptions to explain the spectrum of the hydrogen atom. His simple calculation of its structure agreed superbly with the observed spectrum of hydrogen. That is, he was able to explain why the hydrogen spectrum consists of radiation at only certain discrete wavelengths. Moreover he showed how to calculate those wavelengths with a relatively simple formula.

Bohrs' formula for the wavelengths () of the hydrogen lines is

1/ = R[1/(n_l)² -1/ n(_u)²],

where the n's are the 'quantum' numbers of the orbits n_l is the 'quantum' number of the lower orbit and n_u is the quantum number of the upper orbit. The constant R, known as the Rydberg constant has a value in metric units of 1.097x10⁷ m^-1.

Bohr further showed that the value depends only on fundamental constants of nature such as the electron charge, pi, etc.

For example, if an electron in a hydrogen atom drops from level 4 to level 3, the formula for the wavelength of the emitted light is

1/ = 1.097x10⁷ m^-1x(1/4² -1/3²),1/ = 1.097x10⁷x(1/16-1/9) m^-1.Flipping the equation over so that the wavelength is on top, we get/ = 4.86x10^-7 meters = 486 nanometers,,

which is precisely the wavelength of the blue spectrum line of hydrogen.

For his work, Bohr was awarded the Nobel Prize in Physics in 1922.

The Bohr model of the atom is not only a scientific triumph, but it also illustrates superbly how science works.

Scientists at the end of the 19th century had a model that was unable to explain the observed spectrum of hydrogen. That is, it disagreed with experiment. Bohr proposed revisions to the model. The changes led to a new model that agreed extremely well with the experiments. To go a step further, we might note that advances in the 20th century showed that the Bohr model itself needed revisions. Those have been made and yield even better agreement with experiment. Nonetheless, the Bohr model is still a useful way to picture what is happening in atoms, much as the celestial sphere is a useful way to picture the position of stars and planets on the sky.

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.

(1)

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

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

(

Bohr Atom Theory

2) The force that keeps the electron in its orbit

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

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.

Bohr Atomic Model

(3)

(n is a counting number)

So, rearranging equation (3) gives

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.

R_H 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 )E = (-2.18 x 10^-18) (0.139)E = -3.03 x 10^-19 J
(the negative sign tells us that energy is released)

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).

Bohr Atomic Theory

E_photon = hu

E_photon = 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

l = 656 nm (red)

Bohr Atomic Model Worksheet

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