Antoine Lavoisier:

Antoine Lavoisier (1743-1794) is often called the father of modern chemistry. He is possibly the greatest scientist France ever produced. The son of a wealthy Parisian lawyer, Lavoisier completed a law degree to please his parents, but his real interest was in science. In 1768 he was elected to the prestigious French Academy of Sciences in which he was a rising star, becoming director in 1785.

Peter Atkins, the noted UK chemist, credits Lavoisier as "The Father of Modern Chemistry" for three reasons.

First, Lavoisier introduced a new language of chemistry, which swept away the old terminology based on the natural origins of things, such as flowers and trees - terminologies that said nothing about the chemical composition of the material.

Second, Lavoisier emphasized the fundamental distinction between elements and compounds and established the basic rules of chemical combination. One of his most famous experiments was a public demonstration that water is made up of the two elements, hydrogen and oxygen.

Third, Lavoisier introduced precise measurement into chemistry and so turned it into an exact physical science.

Lavoisier is best remembered for overturning the theory of phlogiston.

Phlogiston was a hypothetical substance, postulated in the 17th century to explain combustion. The theory held that combustible substances contain phlogiston and combustion is essentially the process of losing phlogiston.

The British chemist Joseph Priestley (1733-1804) discovered that air is composed of several gases, one of which is essential to animal life, which Priestley called "dephlogisticated air". He generated it by heating mercuric oxide and collecting the gas that was given off. Priestley showed Lavoisier how to make dephlogisticated air.

Lavoisier re-named dephlogisticated air as oxygen. The emanation of oxygen from mercuric oxide suggested to Lavoisier that chemical decomposition could be quantified. He ran the experiment in both directions. First he burned mercury in oxygen and measured the amount of oxygen that combines with the mercury to make mercuric oxide.

Next he took the mercuric oxide and heated it to expel the oxygen, leaving mercury behind. When he measured the oxygen generated, it was exactly the amount that had been taken up before.

The overall process was revealed as the combination and uncoupling of fixed quantities of mercury and oxygen. Combustion of mercury was revealed as chemical combination with oxygen and therefore, phlogiston was no more. 

Oxygen theory of combustion

During late 1772 Lavoisier turned his attention to the phenomenon of combustion, the topic on which he was to make his most significant contribution to science. He reported the results of his first experiments on combustion in a note to the Academy on 20 October, in which he reported that when phosphorus burned, it combined with a large quantity of air to produce acid spirit of phosphorus, and that the phosphorus increased in weight on burning. In a second sealed note deposited with the Academy a few weeks later (1 November) Lavoisier extended his observations and conclusions to the burning of sulfur and went on to add that "what is observed in the combustion of sulfur and phosphorus may well take place in the case of all substances that gain in weight by combustion and calcination: and I am persuaded that the increase in weight of metallic calces is due to the same cause."

Joseph Black's "fixed air"

During 1773 Lavoisier determined to review thoroughly the literature on air, particularly "fixed air," and to repeat many of the experiments of other workers in the field. He published an account of this review in 1774 in a book entitled Physical and Chemical Essays. In the course of this review he made his first full study of the work of Joseph Black, the Scottish chemist who had carried out a series of classic quantitative experiments on the mild and caustic alkalies. Black had shown that the difference between a mild alkali, for example, chalk (CaCO3), and the caustic form, for example, quicklime (CaO), lay in the fact that the former contained "fixed air," not common air fixed in the chalk, but a distinct chemical species, now understood to be carbon dioxide (CO2), which was a constituent of the atmosphere. Lavoisier recognized that Black's fixed air was identical with the air evolved when metal calces were reduced with the charcoal and even suggested that the air which combined with metals on calcination and increased the weight might be Black's fixed air, that is, CO2.

Joseph Priestley

Joseph Priestley, an English chemist known for isolating oxygen, which he termed "dephlogisticated air."

In the spring of 1774 Lavoisier carried out experiments on the calcination of tin and lead in sealed vessels which conclusively confirmed that the increase in weight of metals in combustion was due to combination with air. But the question remained about whether it was combination with common atmospheric air or with only a part of atmospheric air. In October the English chemist Joseph Priestley visited Paris, where he met Lavoisier and told him of the air which he had produced by heating the red calx of mercury with a burning glass and that released air had supported combustion with extreme vigor. Priestley at this time was unsure of the nature of this gas, but he felt that it was an especially pure form of common air.

Lavoisier carried out his own researches on this peculiar substance. The result was his famous memoir On the Nature of the Principle Which Combines with Metals during Their Calcination and Increases Their Weight, read to the Academy on 26 April 1775. In the original memoir Lavoisier showed that the mercury calx was a true metallic calx in that it could be reduced with charcoal, giving off Black's fixed air in the process. When reduced without charcoal, it gave off an air which supported respiration and combustion in an enhanced way. He concluded that this was just a pure form of common air, and that it was the air itself "undivided, without alteration, without decomposition" which combined with metals on calcination.
After returning from Paris, Priestley took up once again his investigation of the air from mercury calx. His results now showed that this air was not just an especially pure form of common air but was "five or six times better than common air, for the purpose of respiration, inflammation, and ... every other use of common air." He called the air dephlogisticated air, as he thought it was common air deprived of its phlogiston. Since it was therefore in a state to absorb a much greater quantity of phlogiston given off by burning bodies and respiring animals, the greatly enhanced combustion of substances and the greater ease of breathing in this air were explained.

Pioneer of stoichiometry

Lavoisier's researches included some of the first truly quantitative chemical experiments. He carefully weighed the reactants and products of a chemical reaction in a sealed glass vessel so that no gases could escape, which was a crucial step in the advancement of chemistry. In 1774, he showed that, although matter can change its state in a chemical reaction, the total mass of matter is the same at the end as at the beginning of every chemical change. Thus, for instance, if a piece of wood is burned to ashes, the total mass remains unchanged if gaseous reactants and products are included. Lavoisier's experiments supported the law of conservation of mass. In France it is taught as Lavoisier's Law and is paraphrased from a statement in his "Nothing is lost, nothing is created, everything is transformed. Mikhail Lomonosov (1711–1765) had previously expressed similar ideas in 1748 and proved them in experiments; others whose ideas pre-date the work of Lavoisier include Jean Rey (1583–1645), Joseph Black (1728–1799), and Henry Cavendish (1731–1810).

 

Quantum mechanics:

1900 (Planck): Max Planck proposed that light with frequency ν is emitted in quantized lumps of energy that come in integral multiples of the quantity,

                                        E = hν = ¯hω                     (1)

where h ≈ 6.63 · 10−34 J ·s  is Planck’s constant,   and ¯h ≡ h/2π = 1.06 · 10−34 J ·s.

The frequency ν of light is generally very large (on the order of 1015 s−1 for the visible spectrum), but the smallness of h wins out, so the hν unit of energy is very small (at least on an everyday energy scale). The energy is therefore essentially continuous for most purposes. However, a puzzle in late 19th-century physics was the blackbody radiation problem. In a nutshell, the issue was that the classical (continuous) theory of light predicted that certain objects would radiate an infinite amount of energy, which of course can’t be correct. Planck’s hypothesis of quantized radiation not only got rid of the problem of the infinity, but also correctly predicted the shape of the power curve as a function of temperature.

The results that we derived for electromagnetic waves are still true. In particular, the energy flux is given by the Poynting vector  And  E = pc for a light. Planck’s hypothesis simply adds the information of how many lumps of energy a wave contains. Although strictly speaking, Planck initially thought that the quantization was only a function of the emission process and not inherent to the light itself.

1905 (Einstein): Albert Einstein stated that the quantization was in fact inherent to the light, and that the lumps can be interpreted as particles, which we now call “photons.” This proposal was a result of his work on the photoelectric effect, which deals with the absorption of light and the emission of electrons from a material.

We know that  E = pc  for a light wave. (This relation also follows from Einstein’s 1905 work on relativity, where he showed that E = pc for any massless particle, an example of which is a photon.) And we also know that ω = ck for a light wave. So Planck’s      E = ¯hω relation becomes

               E = ¯hω  =⇒     pc = ¯h(ck)  =⇒      p = ¯hk       (2)

This result relates the momentum of a photon to the wavenumber of the wave it is associated with.

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1913 (Bohr): Niels Bohr stated that electrons in atoms have wavelike properties. This correctly explained a few things about hydrogen, in particular the quantized energy levels that were known.

1924 (de Broglie): Louis de Broglie proposed that all particles are associated with waves, where the frequency and wavenumber of the wave are given by the same relations we found above for photons, namely  E = ¯hω  and p = ¯hk. The larger E and p are, the larger ω and k are. Even for small E and p that are typical of a photon, ω and k are very large because ¯h is so small. So any everyday-sized particle with large (in comparison) energy and momentum values will have extremely large ω and k values. This (among other reasons) makes it virtually impossible to observe the wave nature of macroscopic amounts of matter.

This proposal (that E = ¯hω and p = ¯hk also hold for massive particles) was a big step, because many things that are true for photons are not true for massive (and nonrelativistic) particles. For example, E = pc (and hence ω = ck) holds only for massless particles (we’ll see below how ω and k are related for massive particles). But the proposal was a reasonable one to try. And it turned out to be correct, in view of the fact that the resulting predictions agree with experiments.

The fact that any particle has a wave associated with it leads to the so-called waveparticle duality. Are things particles, or waves, or both? Well, it depends what you’re doing with them. Sometimes things behave like waves, sometimes they behave like particles. A vaguely true statement is that things behave like waves until a measurement takes place, at which point they behave like particles. However, approximately one million things are left unaddressed in that sentence. The wave-particle duality is one of the things that few people, if any, understand about quantum mechanics.

1925 (Heisenberg): Werner Heisenberg formulated a version of quantum mechanics that made use of matrix mechanics. We won’t deal with this matrix formulation (it’s rather difficult), but instead with the following wave formulation due to Schrodinger (this is a waves book, after all).

1926 (Schrodinger): Erwin Schrodinger formulated a version of quantum mechanics that was based on waves. He wrote down a wave equation (the so-called Schrodinger equation) that governs how the waves evolve in space and time. We’ll deal with this equation in depth below. Even though the equation is correct, the correct interpretation of what the wave actually meant was still missing. Initially Schrodinger thought (incorrectly) that the wave represented the charge density.

1926 (Born): Max Born correctly interpreted Schrodinger’s wave as a probability amplitude. By “amplitude” we mean that the wave must be squared to obtain the desired probability. More precisely, since the wave (as we’ll see) is in general complex, we need to square its absolute value. This yields the probability of finding a particle at a given location (assuming that the wave is written as a function of x).

This probability isn’t a consequence of ignorance, as is the case with virtually every other example of probability you’re familiar with. For example, in a coin toss, if you know everything about the initial motion of the coin (velocity, angular velocity), along with all external influences (air currents, nature of the floor it lands on, etc.), then you can predict which side will land facing up. Quantum mechanical probabilities aren’t like this. They aren’t a consequence of missing information. The probabilities are truly random, and there is no further information (so-called “hidden variables”) that will make things unrandom. The topic of hidden variables includes various theorems (such as Bell’s theorem) and experimental results that you will learn about in a quantum mechanics course.

1926 (Dirac): Paul Dirac showed that Heisenberg’s and Schrodinger’s versions of quantum mechanics were equivalent, in that they could both be derived from a more general version of quantum mechanics.

The Schrodinger equation

  we’ll give a “derivation” of the Schrodinger equation. Our starting point will be the classical nonrelativistic expression for the energy of a particle, which is the sum of the kinetic and potential energies. We’ll assume as usual that the potential is a function of only x. We have

                      E = K + V = 1 /2 mv2 + V (x) = p2 /2m + V (x).             (3)

We’ll now invoke de Broglie’s claim that all particles can be represented as waves with frequency ω and wavenumber k, and that   E = ¯hω and p = ¯hk.  This turns the expression for the energy into

                   ¯hω = ¯h2 k2 /2m + V (x).                                                    (4)

A wave with frequency ω and wavenumber k can be written as usual as,  ψ(x, t) = Aei(kx−ωt) (the convention is to put a minus sign in front of the ωt). In 3-D we would have  ψ(r, t) = Aei(k·r−ωt) , but let’s just deal with 1-D. We now note that

     ∂ψ /∂t = −iωψ =⇒  ωψ = i ∂ψ /∂t , and ∂ 2ψ /∂x2 = −k2ψ =⇒     k2ψ = − ∂ 2ψ /∂x2 .      (5)

If we multiply the energy equation in Eq. (4) by ψ, and then plug in these relations, we obtain

     ¯h(ωψ) = ¯h2 /2m .(k 2ψ) + V (x)ψ   =⇒     i¯h ∂ψ /∂t = −¯h2 /2m · ∂ 2ψ /∂x2 + V ψ      (6)

This is the time-dependent Schrodinger equation. If we put the x and t arguments back in, the equation takes the form,

                          i¯h ∂ψ(x, t) /∂t = −¯h2 /2m · ∂ 2ψ(x, t) /∂x2 + V (x)ψ(x, t).               (7)

In 3-D, the x dependence turns into dependence on all three coordinates (x, y, z), and the ∂ 2ψ/∂x2 term becomes ∇2ψ (the sum of the second derivatives). Remember that Born’s (correct) interpretation of ψ(x) is that |ψ(x)|2 gives the probability of finding the particle at position x.

Having successfully produced the time-dependent Schrodinger equation, we should ask: Did the above reasoning actually prove that the Schrodinger equation is valid? No, it didn’t, for three reasons.

1. The reasoning is based on de Broglie’s assumption that there is a wave associated with every particle, and also on the assumption that the ω and k of the wave are related to E and p via Planck’s constant in Eqs. (1) and (2). We had to accept these assumptions on faith.

2. Said in a different way, it is impossible to actually prove anything in physics. All we can do is make an educated guess at a theory, and then do experiments to try to show that the theory is consistent with the real world. The more experiments we do, the more comfortable we are that the theory is a good one. But we can never be absolutely sure that we have the correct theory. In fact, odds are that it’s simply the limiting case of a more correct theory.

3. The Schrodinger equation actually isn’t valid, so there’s certainly no way that we proved it. Consistent with the above point concerning limiting cases, the quantum theory based on Schrodinger’s equation is just a limiting theory of a more correct one, which happens to be quantum field theory (which unifies quantum mechanics with special relativity). This in turn must be a limiting theory of yet another more correct one, because it doesn’t incorporate gravity. Eventually, there will be one theory that covers everything (although this point can be debated), but we’re definitely not there yet.

Due to the “i” that appears in Eq. (6), ψ(x) is complex. And in contrast with waves in classical mechanics, the entire complex function now matters in quantum mechanics. We won’t be taking the real part in the end. Up to this point in the book, the use of complex functions was simply a matter of convenience, because it is easier to work with exponentials than trig functions. Only the real part mattered (or imaginary part – take your pick, but not both). But in quantum mechanics the whole complex wavefunction is relevant. However, the theory is structured in such a way that anything you might want to measure (position, momentum, energy, etc.) will always turn out to be a real quantity. This is a necessary feature of any valid theory, of course, because you’re not going to go out and measure a distance of 2 + 5i meters, or pay an electrical bill of 17 + 6i kilowatt-hours.

As mentioned, there is an endless number of difficult questions about quantum mechanics that can be discussed. But in this short introduction to the subject, let’s just accept Schrodinger’s equation as valid, and see where it takes us.

Solving the equation

If we put aside the profound implications of the Schrodinger equation and regard it as simply a mathematical equation, then it’s just another wave equation. We already know the solution, of course, because we used the function ψ(x, t) = Aei(kx−ωt) to produce Eqs. (5) and (6) in the first place. But let’s pretend that we don’t know this, and let’s solve the Schrodinger equation as if we were given it out of the blue. As always, we’ll guess an exponential solution. If we first look at exponential behavior in the time coordinate, our guess is ψ(x, t) = e −iωtf(x) (the minus sign here is convention). Plugging this into Eq. (7) and canceling the e −iωt yields,

                      ¯hωf(x) = − ¯h2 /2m. ∂2f(x) /∂x2 + V (x)f(x).                (8)

But from Eq. (1), we have ¯hω = E. And we’ll now replace f(x) with ψ(x). This might cause a little confusion, since we’ve already used ψ to denote the entire wavefunction ψ(x, t). However, it is general convention to also use the letter ψ to denote the spatial part. So we now have

           E ψ(x) = − ¯h2 /2m. ∂2ψ(x) /∂x2 + V (x)ψ(x)                  (9)

This is called the time-independent Schrodinger equation. This equation is more restrictive than the original time-dependent Schrodinger equation, because it assumes that the particle/wave has a definite energy (that is, a definite ω). In general, a particle can be in a state that is the superposition of states with various definite energies, just like the motion of a string can be the superposition of various normal modes with definite ω’s. The same reasoning applies here as with all the other waves we’ve discussed: From Fourier analysis and from the linearity of the Schrodinger equation, we can build up any general wavefunction from ones with specific energies. Because of this, it suffices to consider the time-independent Schrodinger equation. The solutions for that equation form a basis for all possible solutions.  Continuing with our standard strategy of guessing exponentials, we’ll let ψ(x) = Aeikx. Plugging this into Eq. (9) and canceling the  e ikx  gives (going back to the ¯hω instead of E)

     ¯hω = − ¯h2 /2m (−k2 ) + V (x)    =⇒ ¯hω = ¯h2 k2 /2m + V (x).            (10)

This is simply Eq. (4), so we’ve ended up back where we started, as expected. However, our goal here was to show how the Schrodinger equation can be solved from scratch, without knowing where it came from.

Eq. (10) is (sort of) a dispersion relation. If V (x) is a constant C in a given region, then the relation between ω and k (namely ω = ¯hk2/2m + C) is independent of x, so we have a nice sinusoidal wavefunction (or exponential, if k is imaginary). However, if V (x) isn’t constant, then the wavefunction isn’t characterized by a unique wavenumber. So a function of the form e ikx doesn’t work as a solution for ψ(x). (A Fourier superposition can certainly work, since any function can be expressed that way, but a single e ikx by itself doesn’t work.) This is similar to the case where the density of a string isn’t constant. We don’t obtain sinusoidal waves there either. 

The Origin of the Elements

Quantum Mechanics

 

Quantum mechanics

 Quantum mechanics [part-1]

The special theory of relativity is about the interdependence of space-time relation with reference to different frames of reference.1905 Einstein. the speed of light is always constant, independent of the frame of reference. It makes no difference whether a source of light is stationary or in relative motion.

Quantum mechanics deals with very fast-moving and very small objects, the electromagnetic radiation emitted by the Sun, the photons, as Einstein called it; [like the sub-atomic particles]; unlike the classical physics of large bodies and of relatively slow motions.

Rutherfords conclusion:

Rutherford's Alpha particle scattering experiment.

-Alpha particles are charged helium atoms. 

In doing so he discovered the nucleus of the atom.

The phenomenon of light radiation:

By the end of the 19th century, physicists almost universally accepted the wave theory of light. However, though the ideas of classical physics explain interference and diffraction phenomena relating to the propagation of light, they do not account for the absorption and emission of light.

light also behaves as a particle. dual nature of light. the wave-particle duality. some times light behaves as a wave and sometimes as a particle. but not both at the same time. the particle nature of light is called as, photon.

Photon is a massless particle of energy quantum. Similar to rainwater falling drop by drop. and not continuously.

Quantum mechanics originated from German physicist Planck.

The equation for the quantum of energy is given by the relation,

E = hv where h is a constant called Planck's constant. The value is, h =6.6261 × 10-34 Js.

The photoelectric effect:

Einstein explained photo-electric emission using Planck's concept of energy quanta. light quanta. light is a stream of energy particles called photons.

The phenomenon of emission of electrons from the surface of the metal when the light of suitable frequency falls on it is called the photoelectric effect. The current produced due to emitted electrons is called photocurrent. The photoelectric effect proves the quantum nature of radiation. The relation for a quantum of energy, E = hf is called the Planck-Einstein relation.

Threshold energy. work function.  the Planck-Einsein relation,                 E = hf

                                        Kmax =hf - ɸ    Or    Kmax + ɸ   = hf

Bohr explained the hydrogen atom by placing electrons in discrete energy levels of an atom. the energy of an electron is quantized in an orbital. when an electron jumps from a higher energy state to a lower energy state, it emits energy out as electromagnetic radiation of light. the electron's energy levels are discrete. they are quantized. therefore hydrogen atoms have unique spectral lines.

Max Planck

Planck studied at the Universities of Munich and Berlin, where his teachers included Kirchhoff and Helmholtz, and received his doctorate of philosophy at Munich in 1879.

Planck’s earliest work was on the subject of thermodynamics, an interest he acquired from his studies under Kirchhoff, whom he greatly admired. He published papers on entropy, thermoelectricity, and also on the theory of dilute solutions.

The problems of light radiation processes engaged his attention and he showed that these radiations were to be considered, as electromagnetic in nature. Experimental observations on the wavelength distribution of the energy emitted by a black body as a function of temperature were at variance with the predictions of classical physics.

Planck was able to deduce the relationship between the energy and the frequency of radiation. In a paper published in 1900, he announced his derivation of the relationship: this was based on the revolutionary idea that the energy emitted by a resonator could only take on, discrete values or quanta. The energy for a resonator of frequency v is hv where h is a universal constant, now called Planck’s constant. this constant h opened the door for a new theory called quantum mechanics.

This was not only Planck’s most important work but also marked a turning point in the history of physics. The importance of the discovery, with its far-reaching effect on classical physics, was not appreciated at first. However, the evidence for its validity gradually became overwhelming as its application accounted for many discrepancies between observed phenomena and classical theory. Among these applications and developments may be mentioned Einstein’s explanation of the photoelectric effect.

Planck’s work on the quantum theory, as it came to be known, was summarized in two books Thermodynamics (1897) and Theory of heat radiation (1906).

Max Planck and Black-body radiation 

The central assumption behind his new derivation, presented to the DPG on 14 December 1900, was the supposition, now known as the Planck postulate, that electromagnetic energy could be emitted only in quantized form, in other words, the energy could only be a multiple of an elementary unit: 

             E= hv,       where h is Planck's constant,  ( 6.63×10−34 Js), and ν is the frequency of the radiation. Note that the elementary units of energy discussed here are represented by hν and not simply by ν. Physicists now call these quanta photons, and a photon of frequency ν will have its own specific and unique energy. The total energy at that frequency is then equal to hν multiplied by the number of photons at that frequency.

Planck and Nernst, seeking to clarify the increasing number of contradictions, organized the First Solvay Conference (Brussels 1911).

In recognition of Planck's fundamental contribution to a new branch of physics, he was awarded the Nobel Prize in Physics for 1918 (he actually received the award in 1919).

 

Albert Einstein

In 1896 Albert Einstein entered the Swiss Federal Polytechnic School in Zurich to be trained as a teacher in physics and mathematics. In 1901, the year he gained his diploma, he acquired Swiss citizenship and, as he was unable to find a teaching post, he accepted a position as technical assistant in the Swiss Patent Office. In 1905 he obtained his doctor’s degree.

The photoelectric effect is a phenomenon where electrons are emitted from the metal surface when the light of sufficient frequency is incident upon. The concept of the photoelectric effect was first documented in 1887 by Heinrich Hertz and later by Lenard in 1902. But both the observations of the photoelectric effect could not be explained by Maxwell’s electromagnetic wave theory of light. Hertz (who had proved the wave theory) himself did not pursue the matter as he felt sure that it could be explained by the wave theory.

Einstein resolved this problem using Planck’s revolutionary idea that light behaves as a particle. The energy carried by each particle of light (called quanta or photon) is dependent on the light’s frequency (ν) as   E = hν

Where h = Planck’s constant = 6.6261 × 10-34 Js.

Light, Einstein said, is a beam of particles whose energies are related to their frequencies according to Planck's formula. When the light beam is directed at a metal, the photons collide with the atoms. If a photon's frequency is sufficient to knock off an electron, the collision produces the photoelectric effect.

Since light is bundled up into photons, Einstein theorized that when a photon falls on the surface of a metal, the entire photon’s energy is transferred to the electron. light is a stream of particles, the photons.

A part of this energy is used to remove the electron from the metal atom’s grasp and the rest is given to the ejected electron as kinetic energy. Electrons emitted from underneath the metal surface lose some kinetic energy during the collision. But the surface electrons carry all the kinetic energy imparted by the photon and have the maximum kinetic energy.

We can write this mathematically as:

The energy of photon = energy required to eject an electron (work function) + Maximum kinetic energy of the electron

E = W + KE

hv = W + KE

KE = hv – w

The thresh hold energy needed to liberate an electron is called work function. this defines the minimum critical frequency needed to liberate photo-electrons.

An increase in the intensity of the same monochromatic light (so long as the intensity is not too high, which is proportional to the number of photons impinging on the surface in a given time), increases the rate at which electrons are ejected—the photoelectric current I—but the kinetic energy of the photoelectrons and the stopping voltage remain the same. For a given metal and frequency of incident radiation, the rate at which photoelectrons are ejected is directly proportional to the intensity of the incident light.

Photoemission from atoms, molecules, and solids

Electrons that are bound in atoms, molecules, and solids each occupy distinct states of well-defined binding energies. When light quanta deliver more than this amount of energy to an individual electron, the electron may be emitted into free space with excess (kinetic) energy that is hv higher than the electron's binding energy. The distribution of kinetic energies thus reflects the distribution of the binding energies of the electrons in the atomic, molecular or crystalline system: an electron emitted from the state at binding energy Eb is found at kinetic energy Ek = hv - Eb. This distribution is one of the main characteristics of the quantum system and can be used for further studies in quantum chemistry and quantum physics.

 The Compton Effect

The Compton effect is the term used for an unusual result observed when X-rays are scattered on some materials. By classical theory, when an electromagnetic wave is scattered off atoms, the wavelength of the scattered radiation is expected to be the same as the wavelength of the incident radiation. Contrary to this prediction of classical physics, observations show that when X-rays are scattered off some materials, such as graphite, the scattered X-rays have different wavelengths from the wavelength of the incident X-rays. This classically unexplainable phenomenon was studied experimentally by Arthur H. Compton and his collaborators, and Compton gave its explanation in 1923.

To explain the shift in wavelengths measured in the experiment, Compton used Einstein’s idea of light as a particle. The Compton effect has a very important place in the history of physics because it shows that electromagnetic radiation cannot be explained as a purely wave phenomenon. The explanation of the Compton effect gave a convincing argument to the physics community that electromagnetic waves can indeed behave like a stream of photons, which placed the concept of a photon on firm ground.

Compton effect is a process in which x-rays collide with electrons and are scattered.

By the early 20th century, research into the interaction of X-rays with the matter was well underway. It was observed that when X-rays of a known wavelength interact with atoms, the X-rays are scattered through an angle θ and emerge at a different wavelength related to θ. The experiments had found that the wavelength of the scattered rays was longer (corresponding to lower energy) than the initial wavelength.

In 1923, Compton published a paper in the Physical Review that explained the X-ray shift by attributing particle-like momentum to light quanta (Einstein had proposed light quanta in 1905 in explaining the photo-electric effect, but Compton did not build on Einstein's work). The energy of light quanta depends only on the frequency of the light. In his paper, Compton derived the mathematical relationship between the shift in wavelength and the scattering angle of the X-rays by assuming that each scattered X-ray photon interacted with only one electron. His paper concludes by reporting on experiments that verified his derived relation: 

                                            λ' - λ = h (1-cosθ) /me c

 

• In the Compton effect, X-rays scattered off some materials have different wavelengths than the wavelength of the incident X-rays. This phenomenon does not have a classical explanation.
• The Compton effect is explained by assuming that radiation consists of photons that collide with weakly bound electrons in the target material. Both electron and photon are treated as relativistic particles. Conservation laws of the total energy and of momentum are obeyed in collisions.
• Treating the photon as a particle with a momentum that can be transferred to an electron leads to a theoretical Compton shift that agrees with the wavelength shift measured in the experiment. This provides evidence that radiation consists of photons.
• Compton scattering is an inelastic scattering, in which scattered radiation has a longer wavelength than the wavelength of incident radiation.

The de Broglie hypothesis

De Broglie had intended a career in humanities, and received his first degree in history. Afterwards he turned his attention toward mathematics and physics and received a degree in physics. With the outbreak of the First World War in 1914, he offered his services to the army in the development of radio communications.

His 1924 thesis Recherches sur la théorie des quanta (Research on the Theory of the Quanta) introduced his theory of electron waves. This included the wave-particle duality theory of matter, based on the work of Max Planck and Albert Einstein on light. This research culminated in the de Broglie hypothesis stating that any moving particle or object had an associated wave. De Broglie thus created a new field in physics.

Louis Victor de Broglie was a French physicist and aristocrat who made groundbreaking contributions to quantum theory. In his 1924 Ph.D. thesis, he postulated the wave nature of electrons and suggested that all matter has wave properties. This concept is known as the de Broglie hypothesis, an example of wave-particle duality, and forms a central part of the theory of quantum mechanics.

In 1923, Louis de Broglie proposed a hypothesis to explain the theory of the atomic structure. By using a series of substitutions de Broglie hypothesizes particles to hold properties of waves. Within a few years, de Broglie's hypothesis was tested by scientists shooting electrons and rays of lights through slits. What scientists discovered was the electron stream acted the same way as light, proving de Broglie correct.

He gave the relation λ = h/mv, where λ is the wavelength, h is Planck's constant, m is the mass of a particle, moving at a velocity v. de Broglie suggested that particles can exhibit properties of waves.

 where mv = p is the momentum of the particle. The above equation is called de Broglie equation and 'λ' is called the de Broglie wavelength. Thus the significance of the de Broglie equation lies in the fact that it relates the particle character with the wave character of matter.

 Louis de Broglie, in 1924, stated that a wave is associated with a moving particle (i.e. matter) and so named these waves as matter waves. He proposed that just like the light has dual nature, electrons also have wave-like properties.
The wavelength of a moving particle is given by,   λ = h​/p
where h is Planck's constant and p is the momentum of the moving particle.

de Broglie equation states that a matter can act as waves much like light and radiation, which also behave as waves and particles. The equation further explains that a beam of electrons can also be diffracted just like a beam of light. In essence, the de Broglie equation helps us understand the idea of moving particles of matter having a wavelength.

Experimental Confirmation

In 1927, physicists Clinton Davisson and Lester Germer, of Bell Labs, performed an experiment where they fired electrons at a crystalline nickel target. The resulting diffraction pattern matched the predictions of the de Broglie wavelength. De Broglie received the 1929 Nobel Prize for his theory (the first time it was ever awarded for a Ph.D. thesis) and Davisson/Germer jointly won it in 1937 for the experimental discovery of electron diffraction (and thus the proving of de Broglie's hypothesis).

 The DPG held a celebration, during which the Max-Planck medal (founded as the highest medal by the DPG in 1928) was awarded to French physicist Louis de Broglie.

 

Erwin Schrodinger

In the first years of his career Schrödinger became acquainted with the ideas of the old quantum theory, developed in the works of Max Planck, Albert Einstein, Niels Bohr, Arnold Sommerfeld, and others. This knowledge helped him work on some problems in theoretical physics, but the Austrian scientist at the time was not yet ready to part with the traditional methods of classical physics.

In autumn 1922 he analyzed the electron orbits in an atom from a geometric point of view, using methods developed by the mathematician Hermann Weyl (1885–1955). This work, in which it was shown that quantum orbits are associated with certain geometric properties, was an important step in predicting some of the features of wave mechanics.

Earlier in the same year he created the Schrödinger equation of the relativistic Doppler effect for spectral lines, based on the hypothesis of light quanta and considerations of energy and momentum. He liked the idea of his teacher Exner on the statistical nature of the conservation laws, so he enthusiastically embraced the articles of Bohr, Kramers, and Slater, which suggested the possibility of violation of these laws in individual atomic processes (for example, in the process of emission of radiation).

In January 1926, Schrödinger published in Annalen der Physik the paper "Quantisierung als Eigenwertproblem" (Quantization as an Eigenvalue Problem) on wave mechanics and presented what is now known as the Schrödinger equation. In this paper, he gave a "derivation" of the wave equation for time-independent systems and showed that it gave the correct energy eigenvalues for a hydrogen-like atom. This paper has been universally celebrated as one of the most important achievements of the twentieth century and created a revolution in most areas of quantum mechanics and indeed of all physics and chemistry.

A second paper was submitted just four weeks later that solved the quantum harmonic oscillator, rigid rotor, and diatomic molecule problems and gave a new derivation of the Schrödinger equation. A third paper, published in May, showed the equivalence of his approach to that of Heisenberg and gave the treatment of the Stark effect. A fourth paper in this series showed how to treat problems in which the system changes with time, as in scattering problems. In this paper, he introduced a complex solution to the wave equation in order to prevent the occurrence of fourth and sixth-order differential equations. (This was arguably the moment when quantum mechanics switched from real to complex numbers.) When he introduced complex numbers in order to lower the order of the differential equations, something magical happened, and all of wave mechanics was at his feet. (He eventually reduced the order to one.) These papers were his central achievement and were at once recognized as having great significance by the physics community.

Schrödinger was not entirely comfortable with the implications of quantum theory referring to his theory as “wave mechanics.” He wrote about the probability interpretation of quantum mechanics, saying: "I don't like it, and I'm sorry I ever had anything to do with it." (Just in order to ridicule the Copenhagen interpretation of quantum mechanics, he contrived the famous thought experiment called Schrödinger's cat paradox.)

Erwin Schrödinger proposed the quantum mechanical model of the atom, which treats electrons as matter waves. ... The square of the wave function, ψ2, represents the probability of finding an electron in a given region within the atom.

 

Key points

Louis de Broglie proposed that all particles could be treated as matter waves with a wavelength λ, given by the following equation:              λ= h / mv

• Erwin Schrödinger proposed the quantum mechanical model of the atom, which treats electrons as matter waves.
• Schrödinger's equation, H^ψ =Eψ, can be solved to yield a series of wave function ψ, each of which is associated with an electron binding energy, E.
• The square of the wave function, ψ, squared, represents the probability of finding an electron in a given region within the atom.
• An atomic orbital is defined as the region within an atom that encloses where the electron is likely to be 90% of the time.
• The Heisenberg uncertainty principle states that we can't know both the energy and position of an electron. Therefore, as we learn more about the electron's position, we know less about its energy, and vice versa.
• Electrons have an intrinsic property called spin, and an electron can have one of two possible spin values: spin-up or spin-down.
• Any two electrons occupying the same orbital must have opposite spins.

 

ದಕ್ಷಿಣ ಭಾರತದ ಚಾಲುಕ್ಯರು

ಚಾಲುಕ್ಯರು ದಕ್ಷಿಣ ಪ್ರಸ್ಥಭೂಮಿಯ ಪ್ರದೇಶವನ್ನು ೬೦೦ ವರ್ಷಗಳಷ್ಟು ದೀರ್ಘ ಕಾಲ ಆಳಿದರು. ಈ ಅವಧಿಯಲ್ಲಿ ಮೂರು, ಸ್ವತಂತ್ರ ಆದರೆ ನಿಕಟ ಸಂಬಂಧದ, ರಾಜ್ಯಗಳಾಗಿ ಮೆರೆದಿದ್ದವು. ಇವು ಬಾದಾಮಿಯ ಚಾಲುಕ್ಯರು, (ಕ್ರಿ.ಶ. ೬ - ೮ನೆಯ ಶತಮಾನ) ಮತ್ತು ಅವರದೇ ಸೋದರ ಸಾಮ್ರಾಜ್ಯಗಳಾದ ಕಲ್ಯಾಣಿಯ ( ಪಶ್ಚಿಮ) ಚಾಲುಕ್ಯರು ಮತ್ತು ವೆಂಗಿಯ (ಪೂರ್ವ) ಚಾಲುಕ್ಯರು.

ಕರ್ನಾಟಕದ ಇತಿಹಾಸದಲ್ಲಿ , ಚಾಲುಕ್ಯರ ಕಾಲವನ್ನು ಸುವರ್ಣ ಯುಗವೆಂದು ಪರಿಗಣಿಸಲಾಗಿದೆ. ರಾಜ್ಯವಿಸ್ತಾರ ಅಷ್ಟೇ ಅಲ್ಲದೆ, ಈ ಕಾಲವು ದಕ್ಷ ಆಡಳಿತ ಕ್ರಮ, ಸಾಮಾಜಿಕ ಸುರಕ್ಷತೆ, ವಿದ್ಯಾಪ್ರಸಾರ , ಇತರ ಸಾಂಸ್ಕೃತಿಕ ಚಟುವಟಿಕೆಗಳು, ವ್ಯಾಪಾರ , ವಾಣಿಜ್ಯಗಳಲ್ಲಿ ವಿಕಾಸ , ಸಾಹಿತ್ಯ, ಕಲೆಮತ್ತು ವಾಸ್ತುಶಿಲ್ಪಗಳಲ್ಲಿ ಅಭಿವೃದ್ಧಿ ಇವುಗಳನ್ನೂ ಪ್ರತಿನಿಧಿಸುತ್ತದೆ. ಈ ಕಾಲವು ಸಾಮಾಜಿಕ ಸುಧಾರಣೆಗಳಿಗೂ ಇಂಬು ಕೊಟ್ಟು ಬಸವೇಶ್ವರರಂತಹ ವಿಶಿಷ್ಟ ಸುಧಾರಕರಿಂದ ವೀರಶೈವಪಂಥದ ಹುಟ್ಟಿಗೂ ಕಾರಣವಾಯಿತು"

ಬಾದಾಮಿಯ ಚಾಲುಕ್ಯರು

ಚಾಲುಕ್ಯ ಸಾಮ್ರಾಜ್ಯವನ್ನು ಕಟ್ಟಿದವನು ಒಂದನೆಯ ಪುಲಿಕೇಶಿ (ಕ್ರಿ.ಶ. ೫೫೦). ವಾತಾಪಿ ( ಕರ್ನಾಟಕದ ಬಾಗಲಕೋಟೆ ಜಿಲ್ಲೆಯ ಈಗಿನ ಬಾದಾಮಿ) ಯನ್ನು ವಶಪಡಿಸಿಕೊಂಡು ಅದನ್ನು ತನ್ನ ರಾಜಧಾನಿಯನ್ನಾಗಿ ಮಾಡಿಕೊಂಡ. ಈ ಚಾಲುಕ್ಯರು ಮುಂದೆ ಬಾದಾಮಿಯ ಚಾಲುಕ್ಯರು ಎಂದು ಪ್ರಸಿದ್ಧರಾದರು. ಪುಲಿಕೇಶಿ ಹಾಗೂ ಆತನ ವಂಶಸ್ಥರು ಆಳಿದ ರಾಜ್ಯ ಇಂದಿನ ಸಂಪೂರ್ಣ ಕರ್ನಾಟಕ ರಾಜ್ಯ, ಮಹಾರಾಷ್ಟ್ರ, ಗೋವಾ, ಮಧ್ಯಪ್ರದೇಶ, ಗುಜರಾತ್ ಮತ್ತು ಆಂಧ್ರ ಪ್ರದೇಶದ ಬಹುತೇಕ ಭಾಗಗಳನ್ನು ಒಳಗೊಂಡಿತ್ತು. ಇಮ್ಮಡಿ ಪುಲಿಕೇಶಿ ಬಾದಾಮಿ ಚಾಲುಕ್ಯರ ಅತಿ ದೊಡ್ಡ ಚಕ್ರವರ್ತಿ.

ಕ್ರಿ.ಶ. ೭೫೩ರಲ್ಲಿ ರಾಷ್ಟ್ರಕೂಟರ ದಂತಿದುರ್ಗನು, ಕೀರ್ತಿವರ್ಮನ್ನು ಸೋಲಿಸುವುದರೊಂದಿಗೆ ಈ ಚಾಲುಕ್ಯ ಸಾಮ್ರಾಜ್ಯಕ್ಕೆ ತೆರೆ ಬಿದ್ದಿತು.

ಕಲ್ಯಾಣಿ ಚಾಲುಕ್ಯರು

ರಾಷ್ಟ್ರಕೂಟರ ಕಾಲದಲ್ಲಿ ಹಿಮ್ಮೆಟ್ಟಿದ ಚಾಲುಕ್ಯ ಸಾಮ್ರಾಜ್ಯ, ಚಾಲುಕ್ಯರ ವಂಶಜರಲ್ಲಿ ಒಬ್ಬನಾದ ಎರಡನೇ ತೈಲಪನು,  ಮಾನ್ಯಖೇಡದ ಮೂರನೆಯ ಕೃಷ್ಣನನ್ನು ಪದಚ್ಯುತಮಾಡಿ, ರಾಷ್ಟ್ರಕೂಟರನ್ನು ಸೋಲಿಸಿ ಸುಮಾರು ಕ್ರಿ.ಶ. ೯೭೩ರ ಸಮಯಕ್ಕೆ ಪಟ್ಟಕ್ಕೆ ಬರುತ್ತಾರನೆ. ಚಾಲುಕ್ಯ ರಾಜ್ಯದ ಬಹುತೇಕ ಪ್ರದೇಶಗಳನ್ನು ಮತ್ತೆ ಕೈವಶಮಾಡಿಕೊಳ್ಳುವುದರೊಂದಿಗೆ, ತನ್ನ ವೈಭವವನ್ನು ಮರಳಿ ಪಡೆಯಿತು.  ಇವರು ಮಾನ್ಯಖೇಡವನ್ನು ತಮ್ಮ ಆರಂಭದ ರಾಜಧಾನಿಯಾಗಿ ಮಾಡಿಕೊಂಡು ಆಡಳಿತ ವಿಸ್ತರಿಸುತ್ತಾನೆ. ಇವರಿಗೂ ಚೋಳರಿಗೂ ಪದೇ ಪದೇ ಯುದ್ಧಗಳು ನಡೆಯುತ್ತಿದ್ದವು. ಮೊದಲನೆಯ ಸೋಮೇಶ್ವರ ಎಂಬ ಚಾಲುಕ್ಯ ಅರಸು ರಾಜಾಧಿರಾಜ ಚೋಳ ನನ್ನು ಕ್ರಿ.ಶ. ೧೦೫೨ ರಲ್ಲಿ ಸೋಲಿಸಿದನು. ಚಾಲುಕ್ಯರು ಸೋಮೇಶ್ವರನ ಕಾಲಕ್ಕೆ ತಮ್ಮ ರಾಜಧಾನಿಯನ್ನು ಮಾನ್ಯಖೇಡದಿಂದ ಇಂದಿನ ಕಲ್ಯಾಣಕ್ಕೆ ಸ್ಥಳಾಂತರಿಸುತ್ತಾರೆ. ಚಾಲುಕ್ಯರ ಈ ಶಾಖೆ ಕಲ್ಯಾಣಿಯ ( ಪಶ್ಚಿಮ) ಚಾಲುಕ್ಯರೆಂದು ಹೆಸರಾಯಿತು. ಮುಂದೆ ಸುಮಾರು ೨೫೦ ವರ್ಷ ಆಳಿದ ಈ ರಾಜವಂಶವು , ಚೋಳರೊಂದಿಗೂ , ವೆಂಗಿಯ ಚಾಲುಕ್ಯರೊಂದಿಗೂ ನಿರಂತರ ಹೋರಾಟದಲ್ಲಿ ತೊಡಗಿತ್ತು. ಸತ್ಯಾಶ್ರಯ (ಕ್ರಿ.ಶ. ೯ ೯ ೭-೧೦೦೮), ಒಂದನೆಯ ಸೋಮೇಶ್ವರ (ಕ್ರಿ.ಶ. ೧೦೪೨-೧೦೬ ೮) ಮತ್ತು ಆರನೆಯ ವಿಕ್ರಮಾದಿತ್ಯ (ಕ್ರಿ.ಶ. ೧೦೭೬ – ೧೧೨೬ ) ಈ ವಂಶದ ಕೆಲವು ಪ್ರಸಿದ್ಧ ರಾಜರುಗಳು.

ರನ್ನನಂತಹ ಶ್ರೇಷ್ಠ ಕನ್ನಡ ಕವಿಗಳಿಗೆ ಕಲ್ಯಾಣಿಯ ಚಾಲುಕ್ಯರು ಆಶ್ರಯ ಮತ್ತು ಪ್ರೋತ್ಸಾಹ ಕೊಟ್ಟರು. ರನ್ನನು ಎರಡನೆಯ ತೈಲಪನ ಮತ್ತು ಸತ್ಯಾಶ್ರಯನ ಆಸ್ಥಾನಕವಿಯಾಗಿದ್ದು, ಕಲ್ಯಾಣಿಯ ಚಾಲುಕ್ಯರ ಕಾಲದ ಮೊದಲ ಕವಿ. ಅಜಿತಪುರಾಣ, ಸಾಹಸಭೀಮವಿಜಯ ಅಥವಾ ಗದಾಯುದ್ಧ, ಪರಶುರಾಮಚರಿತ ಮತ್ತು ರನ್ನಕಂದ ಇವನ ಪ್ರಸಿದ್ಧ ಕೃತಿಗಳು.. ಆ ಕಾಲದಲ್ಲಿ ಇನ್ನೂ ಅನೇಕ ಕನ್ನಡ ವಿದ್ವಾಂಸರು ಆಗಿಹೋದರು.

ಕಲ್ಯಾಣಿ ಚಾಲುಕ್ಯರ ರಾಜ ನಾಲ್ಕನೆಯ ವಿಕ್ರಮಾದಿತ್ಯನ ಆಸ್ಥಾನದಲ್ಲಿದ್ದ ಪ್ರಸಿದ್ಧ ಕವಿ ವಿದ್ಯಾಪತಿ ಬಿಲ್ಹಣ, ತನ್ನ ಕೃತಿ ವಿಕ್ರಮಾಂಕದೇವ ಚರಿತೆ ರಚಿಸುತ್ತಾನೆ. ಚಾಲುಕ್ಯ ವಂಶದ ಮುಂದಿನ ಪ್ರಸಿದ್ಧ ಅರಸು ಆರನೇ ವಿಕ್ರಮಾದಿತ್ಯ (ಕ್ರಿ.ಶ ೧೦೭೬-೧೧೨೬, ವಿಕ್ರಮಾಂಕ ಎಂದೂ ಹೆಸರು). ಆರನೆಯ ವಿಕ್ರಮಾದಿತ್ಯನ ಕಾಲಕ್ಕೆ ಇವರ ವೈಭವದ ಕಾಲ ಎನ್ನಬಹುದು. ವಿಕ್ರಮ ಶಕೆಯು ಇವರಿಂದಲೇ ಆರಂಭವಾದದ್ದು. ಕಲ್ಯಾಣಿಯ ಚಾಲುಕ್ಯರು ವಾದಿರಾಜ ( ಯಶೋಧರ ಚರಿತಮ್, ಪಾರ್ಶ್ವನಾಥ ಚರಿತಮ್)ರಂತಹ ಸಂಸ್ಕೃತ ವಿದ್ವಾಂಸರಿಗೆ ಪ್ರೋತ್ಸಾಹ ಕೊಟ್ಟರು. ತನಗೆ ಆಶ್ರಯ ಕೊಟ್ಟ ಆರನೆಯ ವಿಕ್ರಮಾದಿತ್ಯನನ್ನು ಬಿಲ್ಹಣನು ವಿಕ್ರಮಾಂಕದೇವ ಚರಿತೆಯ ಮೂಲಕ ಅಜರಾಮರವಾಗಿಸಿದ್ದಾನೆ. ಸುಪ್ರಸಿದ್ಧ ಮಿತಾಕ್ಷರ ಸಂಹಿತೆ ಬರೆದವನು ವಿಜ್ಞಾನೇಶ್ವರ(ಮರತೂರು). ಸ್ವತಃ ಮೂರನೆಯ ಸೋಮೇಶ್ವರನೇ ಕಲೆ ಮತ್ತು ವಿಜ್ಞಾನದ ಬಗೆಗೆ ವಿಶ್ವಕೋಶವನ್ನು ರಚಿಸಿದನು. ಜಗದೇಕಮಲ್ಲನು ಸಂಗೀತಚೂಡಾಮಣಿಯನ್ನು ರಚಿಸಿದನು. ಕಲ್ಯಾಣದ ಚಾಲುಕ್ಯರು ಸುಮಾರು ೨೫೦ ವರುಷಗಳ ಕಾಲ ಆಳ್ವಿಕೆ ಮಾಡುತ್ತಾರೆ. ಇವರ ಪ್ರದೇಶ ತುಂಗಭದ್ರೆಯಿಂದ ನರ್ಮದೆಯ ವರೆಗೆ ವಿಸ್ತರಿಸಿತ್ತು. ದಕ್ಷಿಣದ ಚೋಳರು ಒಮ್ಮೆ ತುಂಗಭದ್ರೆಯ ವರೆಗೆ ತಮ್ಮ ಸಾಮ್ರಾಜ್ಯ ವಿಸ್ತರಿಸಿದ್ದರು.

ಕಲ್ಯಾಣಿಯ ಚಾಲುಕ್ಯರು ಕರ್ನಾಟಕದ ಧಾರವಾಡ, ಗದಗ ಮತ್ತು ಹಾವೇರಿ ಪ್ರದೇಶಗಳಲ್ಲಿ ಐವತ್ತಕ್ಕೂ ಹೆಚ್ಚು ದೇವಾಲಯಗಳನ್ನು ಕಟ್ಟಿದರು.

ವಿಕ್ರಮಾಂಕನ ಮರಣದ ನಂತರ ಚಾಲುಕ್ಯ ಸಾಮ್ರಾಜ್ಯ ಹೆಚ್ಚು ಕಾಲ ನಿಲ್ಲಲಿಲ್ಲ. 

ಹೊಯ್ಸಳರು, ಕಾಕತೀಯರು ಮತ್ತು ಯಾದವರು ಈ ರಾಜಮನೆತನಗಳ ಉತ್ಕರ್ಷದೊಂದಿಗೆ, ೧೧೮೦ರಲ್ಲಿ, ಕಲ್ಯಾಣಿಯ ಚಾಲುಕ್ಯರ ಸಾಮ್ರಾಜ್ಯವು ಅಸ್ತಂಗತವಾಯಿತು.

ವೆಂಗಿಯ (ಪೂರ್ವ) ಚಾಲುಕ್ಯರು.

ಇಂದಿನ ಆಂಧ್ರ ಪ್ರದೇಶದ ಕರಾವಳಿಯ ಭಾಗವಾಗಿದ್ದ, ವಿಷ್ಣುಕುಂಡಿನ ಸಾಮ್ರಾಜ್ಯದ ಅಳಿದುಳಿದ ಭಾಗಗಳನ್ನು ಸೋಲಿಸಿ, ಇಮ್ಮಡಿ ಪುಲಿಕೇಶಿಯು , ಅಲ್ಲಿಗೆ ತನ್ನ ತಮ್ಮ ಕುಬ್ಜ ವಿಷ್ಣುವರ್ಧನನನ್ನು ರಾಜಪ್ರತಿನಿಧಿಯಾಗಿ ನೇಮಿಸಿದನು. ಪುಲಿಕೇಶಿಯ ಮರಣದ ನಂತರ, ಈ ಶಾಖೆಯು ಸ್ವತಂತ್ರವಾಗಿ, ಮುಖ್ಯ ವಾತಾಪಿ ಸಾಮ್ರಾಜ್ಯಕ್ಕಿಂತ ಮುಂದೆ, ಅನೇಕ ಪೀಳಿಗೆಗಳವರೆಗೆ ಸ್ವತಂತ್ರ ರಾಜ್ಯಭಾರ ಮಾಡಿತು. ಈ ರಾಜರು ೯ ನೆಯ ಶತಮಾನದ ಮಧ್ಯದವರೆಗೂ, ವೆಂಗಿ ಪ್ರಾಂತ್ಯದಲ್ಲಿ ಕನ್ನಡಕ್ಕೆ ಪ್ರೋತ್ಸಾಹ ಕೊಟ್ಟರು. ಅಲ್ಲಿಂದ ಮುಂದಿನ ಶಾಸನಗಳಲ್ಲಿ ಕ್ರಮೇಣ ಕನ್ನಡಲಿಪಿಯಲ್ಲಿ ಬರೆದ ತೆಲುಗು ಭಾಷೆ ಕಾಣಬರುತ್ತದೆ.