Hundred Years Of Atom

K.P.Satheeshsatheeshsithara@gmail.com

I could see farther than others because I stood on the shoulders of giants - Newton

Dalton Thomson Rutherford

These were the giants for Niels Bohr who were the great predecessors of atomic theory

Dalton's Main Postulates

All matter is made up of atoms which are indivisible and indestructible

All atoms of a given element are identical in mass size etc.

Compounds are formed by combination of different kind of atoms

Chemical reaction is a rearrangement of atoms Atoms combine with each other in a fixed

simple whole number ratio

Shortcomings of Dalton's theory

Atoms are actually divisible even though they participate as a whole in chemical reactions

Isotopes and Isobars exist which do not obey Dalton's postulates

In complicated organic compounds atoms do not combine in a simple whole number ratio

Spontaneous nuclear reactions exist

All the defects above was identified only after 1896 and Daltons theory remained intact upto 1896

First clue for the divisibility of atom

Becquerel and curies were the pioneers. 1903 Nobel

Prize for Physics

Atom divides itself spontaneously

without any external influences

Discovery of the Electron (1897)

Cathode ray tube which lead to the discovery of cathode rays which were later shown to beTiny particles and identified as electrons

forming a fundamental constituent of matter

Sir William Crookes (1832 - 1919)

By using Crooke'sTube it was shownThat the rays were

Radiant matter with negative

charge which was very near to the

ideas of Thomson.

Most of the contemporary European scientists considered the rays as disturbances in an ether

medium similar to light

Heinrich Hertz's mistake

1857 - 1894

Hertz in Germany passed these rays through thin gold foils and they readily passed. He did not believe that particles can penetrate through solids. Also he found that the rays are not reflected by electric fields and concluded they are uncharged. The mistake was actually due to the ionized gases neutralising the plates

Thomson's Contribution in 1897Thomson managed to create a very high vacuum

in his tube and succeeded in detecting the deflection of the rays due to the electric field and established that they are negatively charged.

He also showed that they are deflected by a magnetic field by creating a uniform magnetic field using Helmholtz coils.

By adjusting the combined electric and magnetic fields and balancing them to obtain zero deflection he could estimate the velocity of these rays by finding ratio between the fields.

Then by measuring the deflection angle with electric field alone he could estimate the specific charge

Based on several experiments it was thus concluded that the cathode rays are negatively charged particles which Thomson denoted as corpuscles and they are also fundamental constituents of matter and atom is divisible and has an internal structure

From the measurement of specific chargeThomson concluded that the corpuscles areAt lest two thousand times lighter than the Hydrogen atom the lightest particle known At that time.

Extremely small size of the new particle also explained Hertz's observation that cathode Rays penetrated the thin gold foil.

Thus for the first time in the history of science time was ripe enough to create a model for the atom.

History of atom models starts here

In any model building the procedure is to model the system according to the informations available at that point of time. Later when more experimental results Come model will be refined. This actually happened for Atom models also. Story of atom models for last 100 Years is the story of continuous refinement of the model of the microscopic structure of matter.

Some people call this as PLUM PUDDING MODEL

Thomson's Atom Model

Knew that atom consisted of negatively charged particles.

Matter is electrically neutral.

To accommodate this Thomson modelled atom as negative particles in a positive cloud

(1) An atom in which the negatively charged electrons were located within

a continuous distribution of positive charge.

(2) At its lowest energy state, the electrons would be fixed at their

equilibrium positions.

(3) In excited atoms, the electrons would vibrate about their

equilibrium positions.

(4) A vibrating electrons emit electromagnetic radiation.

4.1 Thomsons model (plum pudding)

Plum pudding

A Thomson hydrogen atom has only one characteristic emission frequency conflict with the very large number of different frequencies observed in the spectrum of hydrogen.

Merits and defects

Partly explained the observed periodicity of elements

Modified version of the model explained dispersion of light by dilute gases.

Developed methods for estimating the actual number of electrons in an atom.

At that time spectroscopy was an emerging science and several results about emission and absorption spectra of atoms were known. This could not be explained by Thomson.

Rutherford enters the scene

Geiger and Marsden

After elaborate research In radioactivity Rutherford Had sufficient expertise in creating beam of alpha Particles and he decided to Repeat the gold foil Penetration experiment of Hertz with alpha particles

This task was entrusted to Geiger and Marsden and they submitted the experimental data by 1911 to Rutherford.

Nuclear Physics is Born (1911)

By analysing the scattering data Rutherford concluded that the large angle scattering seen in

the data can be explained only by assuming that

entire mass is concentrated in a small

region.

Elementary method for obtaining this is to develop a constraint for the mass of the target to be very high

compared to the projectile using principle of conservation of momentum and energy

4.2 Rutherfords model

All the positive charge of the atom, and consequently essentially all its mass, are assumed to be concentrated in a small region in the center called the nucleus

(1) Nucleus radius:

(2) Maximum deflection angle:m 10 :Rutherford

m 10 :Thomson14

10

=

=

r

r

rad 1 :Rutherfordrad 10 :Thomson 4

=

=

Rutherford Atom model

4.3 The stability of the nuclear atom

The serious difficulties in the previous atomic model:

(1) The charged electrons constantly accelerate in their motion around

the nucleus, radiate energy in the form of electromagnetic radiation.

The atom would rapidly collapse to nuclear dimension.

(2) The continuous spectrum of radiation is not in agreement with the

discrete spectrum observed in experiments.

4.4 Atomic spectra

An apparatus for measuring atomic spectra

bnamR

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Niels Bohr shoulders the challenge

Bohr's Postulates

N Bohr, Philos. Mag. Vol.26, pp.125, pp.476500, pp.857875, 1913.

1. Atomic electrons move in circular orbits about a massive nucleus under the influence

of the Coulomb attraction between the electron and the nucleus,

2. Instead of the infinity of orbits which would be possible in classical mechanics, an electron can in fact only move in an orbit for which its angular momentum L is quantized

3. Even though it is constantly accelerating, an elec- tron moving in such an allowed orbit does not ra- diate electromagnetic energy.

4. Electrons can only gain or lose energy by jump- ing from one allowed orbit to another, absorb- ing or emitting electromagnetic radiation with a Frequency obeying Plancks law.

These postulates are an unusual mix of Classical mechanics and old quantum theory which most of the contemporaries Of Bohr did not completely accept. But the unprecedented success of the theory was appreciated by all.

4.6 Bohrs model

2220

42

20

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02

02

02

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:energy Total

2421 :energy Kinetic

44 :energy Potential

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1

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pi

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pipipi

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ground state

Value of Rydberg constant accuracy 0.001%

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)4

1(for

)11(

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Lyman

Balmer

Pachen

In the Rydberg formula, the transitions to the groundstate

(i.e., ni = 1, nf = 2, 3, 4, ...) are known as the Lyman series. All lines in this series are in ultraviolet

region with wavelengths ranging from 1216 to912Angstroms.

On the otherhand, the transitions to the first excited state (i.e., ni =2, nf = 3, 4, 5, ...) constitute the

Balmer series. Four of these lines are in the visible region with wave-lengths ranging From 6562 to 4101 Angstroms while the other lines are in the ultraviolet region. Transi-tions to the second excited state (i.e., ni = 3, nf = 4, 5,6,

) constitute the Paschen series and all the wave-lengths

are in the infrared region.

It is interesting to note here that in his First paper, Bohrhad also put forward the celebrated CorrespondencePrinciple which states that the laws of quantum physicsmust reduce to those of classical physics when quantumnumbers such as n become very large.

The incredible thing was that while the proof was given for large n, the final result is claimed to be true for any value of n. What luck that it could work!

Later on, when Bohr made acorrection for finite nuclear mass,i.e., substituted m by the reduced mass he found that the theoretical and experimental values of RH agree to within three parts in 100,000!

4.7 Correction for finite nuclear mass

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222

Another success of the Bohr model wasabout star Zeta Puppis. Before Bohr, it had been Wrongly interpreted as a new series of lines of hydrogen. It was another triumph for the Bohr model that it could explain these lines as those belonging to the spectra of ionized Helium.

It may be noted here that till that timethe spectral lines of ionized helium had not yet been observed in the laboratory. But as soon as this was done,the Bohr model was regarded as a great success.

Yet another triumph was the explanation due to Mosley about the characteristic K alpha lines of X-rays using Bohr's theory

I might add here that while the most compelling ofBohr's results was the derivation of the Balmer formulaof 1885, Bohr claimed throughout his life that he wasunaware of the formula until he was already well alongin the development of his theory. This appears rather strange given the fact that Balmer's work was extensively discussed during major international physics conferences in 1890 as well as in subsequent years

How was the Bohr model received by the physics Community?

Sommerfeld immediately wrote a letter to Bohr,complimenting him for calculating the empirical Ryd-berg constant in terms of the more fundamental con-stants, though he was skeptical about the atomic Model in general.

Einstein too immediately recognized the importance of Bohr's theory saying it was a major development.

4.8 Atomic energy states

Franck -Hertz experiment (1914): the quantized atomic energy

potential retarding :Vpotential ngaccelerati :V

r

4.9 eVHg

Energy level of Hg vapor

9.8 eV

4.8 Interpretation of the quantization rules

Wilson-Sommerfeld quantization rules:

For every physical system in which the coordinates are periodic functions of time, there exists a quantum condition for each coordinate. The quantum conditions are hndqp qq =

:

:

: :

q

n

qpq

q

q

one of the coordinate

the momentum associated with the coordinate

the integer quantum number

the integration over one period of the coordinate

Some Mysteries:Bohrs quantization of the angular momentum?

Plancks quantization of the energy?

Sommerfeld made significant progress over the Bohr model. Further, Sommerfeld removed the degeneracy in the hydrogen atom spectrum by treatingthe problem relativistically thereby explaining the finestructure observed experimentally. Note that the Bohr model was unable to explain the Fine structure observed in the spectrum of the hydrogen atom.Further, Sommerfeld's approach could explain the Starkand the Zeeman effects in hydrogen. After reading these papers, Bohr wrote a letter to Sommerfeld saying I donot believe ever to have read anything with more joythan your beautiful work.

What were the eventual failures of the Bohr-Sommerfeldapproach? While this approach was reasonably suc-cessful for atoms with one valence electron, it failed toexplain much of the spectra of atoms containing morethan one electron. Even for the hydrogen atom, theBohr model gives incorrect value for the orbital angu-lar momentum of the ground state. Broadly speakingthe Bohr-Sommerfeld approach was fundamentally in-consistent and led to many paradoxes. The framework they proposed, a classical description of atoms to which quantization rules were added, was finally rendered untenable.Eventually more accurate atom model base on quantum mechanics emerged.

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