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  • If we consider a thought experiment for determining position of an electron by using photons of light. According to principles of optics, if we use light of wavelength $\lambda$, then the position of electron cannot be located more accurately than + or - $\lambda$. The shorter the wavelength, the greater is the accuracy. Therefore, to observe the position of the electron accurately, light of approximately small wavelength should be used. But the photons of radiations of smaller wavelength will have higher momentum. When even a single photon of this light strikes against it, a large amount of momentum will be transferred to the electron at the time of collision. This will result into greater uncertainty in velocity or momentum.

  • On the other hand, in order to minimize the change in momentum we have to use light having photons with small values of momentum. This will require radiations of larger wavelengths (low momentum), the velocity or momentum will not change appreciably but we will not be able to measure the position accurately with larger wavelength. Therefore, uncertainty in position will increase. Thus, we cannot simultaneously measure the position and momentum of a small moving object like electron accurately. However, in case of macroscopic objects, the position and velocity of the objects can be determined accurately because in these cases, during the interaction between the object and the measuring device, the changes in position and velocity are negligible.

What I explained above is actually the Heisenberg's Uncertainty principle which states that

it is not possible to measure simultaneously both the position and momentum (or velocity) of a microscopic particle, with absolute accuracy.

According to Bohr, the electrons revolve around the nucleus in certain well defined circular orbits. But the idea of uncertainty in position and velocity is said to overrule the Bohr's idea of uncertainty picture of fixed circular orbits.

We may not be able to design an experiment (until now) to measure simultaneously both the position and momentum for the electron. But we cannot overrule Bohr's idea of fixed orbits because of this reason. Because, we may not know whether electrons are revolving in fixed orbits, if are able to locate electrons without using photons. Thus, this could not be the exact reason for overruling the idea of fixed orbit.

So, is there any reason for overruling the idea of fixed orbit? or is there any thing wrong in my opinion about the concept, if so please explain, so that I would not proceed with that wrong thinking?

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What is your question exactly, it's hard to follow. –  boyfarrell Dec 7 '13 at 13:38
    
Thank you for the comment. What I meant to ask is, Bohr's idea of fixed orbits was rejected considering the fact that we can't measure simultaneously both position and momentum of electron. If we tried to locate an electron moving in orbit using photons, it would just get displaced or else there will be difficulty in determining the velocity of electron. So, we would not find electrons in fixed orbits if we try to locate. But we may not know electrons would be moving in fixed orbits, if it is possible to locate electron without using photon...... –  Godparticle Dec 7 '13 at 14:06
    
....Thus, we can't say electrons are not moving in fixed orbits because of this in ability of determining electrons location. So, is there any other reason for rejecting Bohr's idea of fixed orbits? –  Godparticle Dec 7 '13 at 14:08
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4 Answers 4

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So, is there any reason for overruling the idea of fixed orbit? or is there any thing wrong in my opinion about the concept, if so please explain, so that I would not proceed with that wrong thinking?

An insurmountable problem with the Bohr atom is that one has two charged particles orbiting around each other. Electromagnetism was an exact science at that time. A charged particle moving in an electric field ( one moving in the field of the other) would have to radiate energy away, finally falling into the nucleus, if there were no laws that did not allow it to radiate. Thus within the laws of classical physics fixed orbits were an impossibility.

Postulating that X electrons orbiting around Y protons can orbit without radiating was necessary, but not general enough to be called a theory.

The theory that emerged from the plethora of experimental data studying the small dimensions of the atoms was quantum mechanics. It is now understood by physicists that the underlying stratum of nature behaves according to the rules of quantum mechanics, and that classical mechanics and classical electrodynamics are emergent theories from this basis.

Generally, quantum mechanics does not assign definite values. Instead, it makes a prediction using a probability distribution; that is, it describes the probability of obtaining the possible outcomes from measuring an observable. Often these results are skewed by many causes, such as dense probability clouds. Probability clouds are approximate, but better than the Bohr model, whereby electron location is given by a probability function, the wave function eigenvalue, such that the probability is the squared modulus of the complex amplitude, or quantum state nuclear attraction.Naturally, these probabilities will depend on the quantum state at the "instant" of the measurement. Hence, uncertainty is involved in the value. There are, however, certain states that are associated with a definite value of a particular observable. These are known as eigenstates of the observable ("eigen" can be translated from German as meaning "inherent" or "characteristic").

The simplest mathematical formulation for solving for an electron around a nucleus is the Schrodinger equation with the appropriate potential. The solutions reproduce the experimental observations and allow for predictions for other potentials and situations. What is calculated instead of an orbit, is an orbital , a locus in space and time where the electron can be found if measured with a probability given by the square of the wave function.

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Thank you for the answer. I understood that there was a radiation problem with respect to Bohr's model containing circular orbits. Now, I will try to learn how quantum mechanical model overrules radiation problem with orbital concept. –  Godparticle Dec 8 '13 at 18:19
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The reason Bohr's theory is considered surpassed is that Heisenberg and Schroedinger developed more powerful theories, in which Bohr orbits do not play major role. Bohr's theory works nice only for few-electron systems, like hydrogen atom or ion Li$^{2+}$. For more complicated systems like the molecule of water H$_2$O it is difficult to see how to generalize the concept of Bohr orbits to them. On the other hand, the Schroedinger equation generalizes easily to any number of electrons and nuclei.

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I'd say not few electron systems, but one electron systems. –  Ruslan Dec 7 '13 at 22:58
    
You're probably right, although I remember seeing some paper which applied some kind of Bohrian orbits to helium with good success (I cannot find the paper but you can find similar ones on the Internet.) There is also similar approach called "semi-classical theory of helium" - check scholarpedia.org/article/Semiclassical_theory_of_helium_atom –  Ján Lalinský Dec 8 '13 at 1:06
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I don't think you really understood the outcome of the discussion Is uncertainty principle a technical difficulty in measurement?.

This has nothing to do with our ability to perform a precise measurement. The position and momentum of the electron simply does not exist simultaneously in a definite state. It is like trying to measure the exact day that winter falls on :)

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Thank you for the answer. I will try to understand it, if not possible, I hope physics stack exchange will help me. Up to the extent what I have understood, as you said position and momentum of electron simply does not exist simultaneously in definite state if photons are used to investigate.As said before, using photons to know the location displaces electrons from the fixed orbit (if assumed orbits exist). If we can develop an experiment to determine the location without using photon, we may not have the displacement and uncertainty. So, we can't refuse Bohr's idea based on uncertainty –  Godparticle Dec 7 '13 at 15:36
    
No, photons have nothing to do with it. The position and momentum of the electron itself does not exist simultaneously in a definite state. One, or the other, or somewhere in between, but not both at the same time. It has nothing to do with our ability to measure (using photons or cleverness or elves). Electrons aren't simply tiny little charged balls, and if you try to think of them as such then you are missing the essence of quantum mechanics. –  lionelbrits Dec 7 '13 at 17:00
    
To give you an example, an electron can be in a superposition of two states, one where it is over here, and one where it is over there, 10 meters away. What would you like to say it's position is, exactly? –  lionelbrits Dec 7 '13 at 17:01
    
Thank you for the healthy discussion. I hope I can ask a doubt for you. I thought photon plays a major role here, which is in opposition with your statement. I thought position and momentum of electron does not exist only if we use light (photon) to see them. Yes, we can't see any thing with out using light. But even then we can expect any clever idea in the following year. I don't know what I said is correct or wrong. If it is wrong, please explain how position and momentum does not exist even if we don't use light. –  Godparticle Dec 8 '13 at 2:09
    
As an aside, you should say question rather than doubt. Position and momentum are observables, and the values they take are eigenvalues of the position and momentum operators (like matrices). It is not necessary that a vector be an eigenvector of two matrices at the same time. Look up "incompatible observables" –  lionelbrits Dec 8 '13 at 16:18
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In Bohr's theory the smallest possible orbital angular momentum is $\hbar$. The measured value is $0$. On the other hand the picture developed by solving the (time independent) Schödinger equation reproduces the energy levels from Bohr's model and gets the minimum angular momentum and the angular momentum step size right (it also fives you the quantization of the projections of the angular momentum). Add Pauli exclusion to the Schroödinger picture and you can get the shell filling rules and explain why the periodic table has the structure that it does which is another thing that Bohr's atom couldn't do correctly.

Bohr is out because it makes incorrect prediction.

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