Bohrs Atomic and the History

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NEILS BOHR AND ATOMIC PHYSICS

INTRODUCTION

Niels Hendrik David Bohr is the one, who made contributions

to understanding atomic structure and quantum mechanics, for which

he received the Nobel Prize in Physics in 1922. Bohr was born in

Copenhagen, Denmark in 1885. His father (Christian Bohr), was a

professor of physiology at the University of Copenhagen and his

mother (Ellen Adler Bohr), came from a wealth Jewish family. His

brother was Harald Bohr, a mathematician and Olympic footballer

who played for Danish nation. Bohr married with Margerthe Norlund in 1912. He had six

children; one of his sons (Aage Neils Bohr) also received the Nobel Prize in 1975. In year 1903,

Bohr enrolled as an undergraduate at Copenhagen University, initially studying philosophy and

mathematics. In 1905, prompted by a gold medal competition sponsored by the Danish Academy

of Sciences and Letters, he conducted a series of experiments to examine the properties of

surface tension, using his father¶s laboratory in the university. As a student under Christian

Christiansen, he received his doctorate in 1911. As a post-doctorial student, Bohr first conducted

experiments under J.J Thomson at Trinity College, Cambridge. Then, he went study under Ernest

Rutherford at the University of Manchester in England. On the basis of Rutherford¶s theories,

Bohr published his model of atomic structure in 1913, introducing the theory of the electrons

traveling in the orbits around the atom¶s nucleus, the chemical properties of the element being

largely determined by the number of electrons in the outer orbits. Bohr also introduced the idea

that an electron could drop from a higher energy orbital to a lower orbital, emitting o photon

(light quantum) of discrete energy.



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THE SIGNIFICANCE AND THE CONTRIBUTION

In 1913, Bohr published a theory based on earlier theory of Rutherford¶s in the structure

of the atom. Rutherford¶s theory stated that atoms consist of positively charges nucleus, with

negatively charges electrons in orbits around it. Bohr expended the theory by saying that electron

travel only in certain successively larger orbit. He suggests the outer orbits could hold more

electrons then the inner ones and these outer orbits determine the chemical properties of an atom.

Bohr also describe the way atoms emit radiation, by suggesting that when electrons jump from

an outer orbits to an inner orbits, its emit light.

Contribution to Physics:

o The Bohr Atomic Model tells us about the electrons that travel in discrete orbits around

the atom¶s nucleus.

o The Shell Model of Atom, where the chemical properties of an element are determined

by the neutrons on the outermost orbit.

o The correspondence principle, the basis tool of old quantum theory.

o The liquid drop model of the atomic nucleus.

The most important properties of atomic and molecular structure may be exemplified using a

simplified picture of an atom that is called the µBohr Model¶. This model was propose by Bohr in

1915; it is not completely right, but it has many feature that are approximately correct and its

sufficient for our discussion. The correct theory is called µQuantum Mechanics¶; the Bohr Model

an approximation to quantum mechanics that have the virtue of being much simpler.



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THEORY AND RELATED BASICS

Bohr¶s Atomic Model:

Bohr states that the matter is made by the elementary

and the discrete units called as atom. Atoms come from Greek

work µAtomos¶ means invisible. Further studied shows that

atom is not invisible, it is divisible in the fundamental particles

names as protons, electrons and neutrons. In this theory this

electrons exhibits the properties of both as a wave and as a

particle. Hence, the electrons show the dual nature at a single time, means the electron have

some momentum and the position at the same time. The Bohr¶s model describes that there is a

possibility to find the electron in any particular circular orbit. Neils Bohr provided an

explanation of the atomic spectra. Using the simplest atom, hydrogen, Bohr developed a model

of an atom¶s structure in an attempt to explain why the atom was stable.

He proposed a quantum approach to the motion of electrons within the atom and he

postulated that:

o The electrons move only in certain circular orbits, called stationary state or energy

levels. When the electron is orbiting in one of these orbits, it does not radiate

energy.

o The only allowed orbital are those with discrete set of numbers for which the

angular momentum of the electron equals an integral multiple of (h/2 ).

o Emission and absorption of electromagnetic radiation occurs only when an

electron makes a transition from one allowed orbital to another. The frequency of



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Inner orbital

Outer orbital

Electron

transition

Inner orbital

Outer orbital

Electron

transition

the emitted electromagnetic radiation is given by hf = E i - E f where E i is the initial

energy state and E f is the final energy state (refer diagram below).

Formula: where, h = Planck constant (6.626x10

-34Js)

c = speed of light (3.00x108ms-1)

= wavelength

In each case the wavelength of the emitted or absorbed light is exactly such that the

photon carries the energy difference between the two orbits. This energy may be calculated by

dividing the product of the Planck constant and the speed of light ( hc) by the wavelength of the

light.

To summarize, Bohr postulate was that atoms only exist in certain stationary state

characterized by a certain allowed orbits for their electrons, which move in these orbits with

certain amounts of total energy, the so-called energy levels of the atom. When Bohr assumed

these three postulates he considered the atom have one electron of charge ±e and mass m and the

electron move in a circular orbit of radius r around a positively charged nucleus with the velocity

Transition of electron from a higher energy state to a lower energy state will emit radiation where¶s

transition of electron from a lower energy state to a higher energy state will absorb radiation.

Electron

Proton

Neutron

radiation inradiation out



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Electron

v. The electron moves in circular orbits the nucleus under the influence of the Coulomb force of

attraction. The Coulomb force provides the centripetal acceleration.

Energy Level of Hydrogen Atom:

When Bohr assumed the three postulates, the nation that atoms can have quantized

energy levels that were whole number a multiple (n) of hf was widely accepted. Planck

recognized that h had the units of energy multiplied by time (Js) and this is equivalence to

momentum multiple by distance. For an electron in the nth circular orbits of radius r n, the

distance travelled per revolution is 2 r n. Since momentum is p = mevn then the (momentum imes

distance) for each orbit would equal a whole number multiple of h, example:

( mevn )( 2r n ) = nh

Rearrange the formula we will get

( mevnr n ) = nh/2

Where this is the angular momentum (Ln ) of the orbiting electron and n = 1,2,3,«

Protonr

M



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Each value of n corresponding to a permitted value of the orbit radius, which we denote with r n.

When a particle with mass, m moves with speed vn, in a circular orbit with radius r n, its radial

inward acceleration is (vn2 /r n). Newton¶s second law state that a radial inward net force with

magnitude ( F = mvn2 /r n) in needed to cause this acceleration. In hydrogen, the force F is

provided by the electrical attraction between the positive proton and the negative electron. From

Coulomb¶s law we have

The ground state energy (n=1) for hydrogen turns out to be equal to -13.6 eV. The first

excited stated (n=2) of the hydrogen atom has energy of -13.6/22

eV, or 3.40 eV and followed by

the formula:

where n = 1,2,3,«.

Energy level of the hydrogen atom



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Line Spectrum:

The origin of the line spectra can be understood in general terms on the basis of two

central ideas. One is the photon concept and the other is concept of energy levels in an atom. The

line spectrum of an elements results from the emission of photons with specific energies from the

atom. When the photon is emitted, the internal energy of the atom changes by an amount equal

of the energy of the photon. According to Bohr each atom can exist only with certain specific

value of internal energy. Each atom has a set of possible energy level. The electron in an atom

can make a transition from one energy level to a lower level by emitting a photon with energy

equal to energy difference between the initial and the final levels. If E i is initial energy of the

atom before the transition and E f is the final energy of an atom after transition, and the photon

energy is hf =hc/, the conservation of energy gives

Where n f and ni are, respectively, the quantum numbers of the final and initial energy state

involved in the transition. We can rewrite the equation

R takes the value of

Spectral series for hydrogen are also known as Balmer, Lyman, Paschen, Brackett and Pfund

series. The Lyman series is the ultraviolet. Paschen, Brackett and Pfund series is in the infrared.



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APPLICATION

The Bohr Model is commonly introduces the students to Quantum Mechanics, before

moving in the more accurate and more complex electron valence atom. In Bohr Atomic Model

somehow show the electron in hydrogen in a spherical cloud of probability which grows denser

near the nucleus. The rate of decay in hydrogen is equal to the Bohr radius, but since Bohr

worked with circular orbits, not zero area ellipses, the fact that these two numbers exactly agree

is a coincidence.

Most of the spectra atoms are larger. The best that Bohr can make prediction about is K-

alpha and some L-alpha of X-ray emission spectra for larger atom. Emission spectra for atom

with a single outer-shell electron can be approximately predicted. Also, if the empiric electron-

nuclear screening factors for many atoms are known, many other spectral lines can be deduced

from the information, in similar atoms of differing elements, via the Ritz-Rydberg combination

principles.

The Zeeman Effect is the changes in the spectral lines due to external magnetic fields;

these are also due to more complicated quantum principles interacting with electron spin and

orbital magnetic field.

Elliptical orbits with the same energy and quantized angular momentum Several

enhancements to the Bohr model were proposed; most notably the Sommerfeld model or Bohr-

Sommerfeld model, which suggested that electrons travel in elliptical orbits around a nucleus

instead of the Bohr model's circular orbits. This model supplemented the quantized angular

momentum condition of the Bohr model with an additional radial quantization condition, the

Sommerfeld-Wilson quantization condition where p is the momentum canonically conjugate to



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the coordinate q; the integral is the action of action-angle coordinates. This condition is the only

one possible, since the quantum numbers are adiabatic invariants.

The Bohr-Sommerfeld model was fundamentally inconsistent and led to many paradoxes.

The azimuthal quantum number measured the tilt of the orbital plane relative to the x-y plane,

and it could only take a few discrete values. This contradicted the obvious fact that an atom

could be turned this way and that relative to the coordinates without restriction. The Sommerfeld

quantization can be performed in different canonical coordinates, and gives answers which are

different. The incorporation of radiation corrections was difficult, because it required finding

action-angle coordinates for a combined radiation/atom system, which is difficult when the

radiation is allowed to escape. The whole theory did not extend to non-integrable motions, which

meant that many systems could not be treated even in principle. In the end, the model was

replaced the modern quantum mechanical treatment of the hydrogen atom, which was first given

by Wolfgang Pauli in 1925, using Heisenberg's matrix mechanics. The current picture of the

hydrogen atom is based on the atomic orbitals of wave mechanics which Erwin Schrodinger

developed in 1926.

However, this is not to say that the Bohr model was without its successes. Calculations

based on the Bohr-Sommerfeld model were able to accurately explain a number of more

complex atomic spectral effects. For example, up to first-order perturbation, the Bohr model and

quantum mechanics make the same predictions for the spectral line splitting in the Stark effect.

At higher-order perturbations, however, the Bohr model and quantum mechanics differ, and

measurements of the Stark effect under high field strengths helped confirm the correctness of

quantum mechanics over the Bohr model. The prevailing theory behind this difference lies in the



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shapes of the orbitals of the electrons, which vary in shape according to the energy state of the

electron.

The Bohr-Sommerfeld quantization conditions lead to questions in modern mathematics.

Consistent semiclassical quantization condition requires a certain type of structure on the phase

space, which places topological limitations on the types of symplectic manifolds which can be

quantized. In particular, the symplectic form should be the curvature form of a connection of a

Hermitian line bundle, which is called a prequantization.



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IMPACT ON THE SOCIETY

Bohr effect is a property of hemoglobin first described in 1904 by the Danish

physiologist Christian Bohr (father of Niels Bohr), which states that an increasing concentration

of protons or carbon dioxide will reduce the oxygen affinity of hemoglobin. Increasing blood

carbon dioxide levels can lead to a decrease in pH because of the chemical equilibrium between

protons and carbon dioxide.

In deoxyhemoglobin, the N-terminal amino groups of the -subunits and the C-terminal

Histidine of the -subunits participate in ion pairs. The formation of ion pairs causes them to

decrease in acidity. Thus, deoxyhemoglobin binds one proton for every two O2 released. In

oxyhemoglobin, these ion pairings are absent and these groups increase in acidity.

Consequentially, a proton is released for every two O2 bound. Specifically, this reciprocal

coupling of protons and oxygen is the Bohr Effect which combines with bicarbonate to drive off

carbon dioxide in exhalation. Since these two reactions are closely matched, there is little change

in blood pH.

The dissociation curve shifts to the right when carbon dioxide or hydrogen ion

concentration is increased. This facilitates increased oxygen dumping. This mechanism allows

for the body to adapt the problem of supplying more oxygen to tissues that need it the most.

When muscles are undergoing strenuous activity, they generate CO2 and lactic acid as products

of cellular respiration and lactic acid fermentation. In fact, muscles generate lactic acid so

quickly that pH of the blood passing through the muscles will drop to around 7.2. As lactic acid

releases its protons, pH decreases, which causes hemoglobin to release ~10% more oxygen.



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Carbon dioxide modulates O2 binding to hemoglobin directly by combining reversibly to

N-terminal amino groups of blood proteins to form carbamates:

RíNH2 + CO2 RíNHíCOO-+ H

+

Deoxyhemoglobin binds to CO2 more readily to form a carbamate than oxyhemoglobin.

When CO2 concentration is high (as in the capillaries), the protons released by carbamate

formation further promotes oxygen release. Although the difference in CO2 binding between the

oxy and deoxy states of hemoglobin accounts for only 5% of the total blood CO2, it is

responsible for half of the CO2 transported by blood. This is because 10% of the total blood CO2

is lost through the lungs in each circulatory cycle.



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CONCLUSIONS

As a conclusion, Bohr Atomic Model help explain that the electron evolve around the

nucleus in the fix orbital, which specify the Rutherford¶s Atom Model who state that the electron

evolve around the nucleus only and he did not explain why the electron the electrons falls into

the nucleus after spending the energy. Bohr comes out with the theory that helps us understand

more about the electron orbiting the nucleus.



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REFERENCES

1. Dr. Zainal Abidin Sulaiman & Co. 2007. College Matriculation Physics. Selangor. IPTA

Publications.

2. Herman Feshbach, Tetsuo Matsui, Alexandra Oleson. 1988. Neils Bohr: Physics and The

World. Harwood Academic Publishers.

3. http://www.tutorvista.com/physics/niels-bohr-atomic-theory. Download 24th August 2010.

12:28 pm

4. http://www.exampleessays.com/viewpaper/83669.html. Download 24th August 2010.

12:30 pm

5. Murdoch Dugald (2000) "Bohr" in Newton-Smith, N. H. (ed.) A Companion to the

Philosophy of Science. Great Britain: Blackwell Publishers.

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Bohrs Atomic and the History

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