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PowerPedia:Successes of the Bohr atom

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In the Bohr model of hydrogen atom a corpuscular electron turns about a proton. There are several orbits, which radii are R= n2, where n = 1, 2, 3, 4, 5... The first orbit near to proton is called “fundamental?, and it is designated by n=1. The other ones are n=2, n=3, etc.

The electron can jump from one orbit to another. When the electron jumps between two orbits, the hydrogen atom emits a photon ( see the first figure in http://en.wikipedia.org/wiki/Bohr_model ).


Contents

The two forces acting on the electron

Imagine that the electron jumps from the orbit n=2 to the orbit n=4. When the electron performs this jumping, the hydrogen atom emits a photon which wavelenght was calculated by Bohr in the following way:

  • a) he considered that in the orbit n=2 the electron (in the instant when it jumps) is under the action of two forces, FE and FC, that are in equilibrium.
  • b) FE is the electric force of attraction between the proton and the electron, and FC is the centripetal force due to electron’s circular motion.
  • c) And in the orbit n=4 the electron is also under the action of two forces F’E and F’C that are in equilibrium.


Other photons can be emitted, for instance when the electron jumps from n=1 to n=2, or from n=1 to n=3, etc. But the calculus always considers that the electron is in equilibrium between two forces, the electrical and the centripetal, when the atom emits a photon.


Therefore, in the Bohr’s model the centripetal force has
some misterious connection with the emission of photons


Bohr model replaced by the atom of Quantum Mechanics

When the atoms of a gas are excited (for example by an electric discharge), they emit light. After passing through a prism, and projected in a screen, the light appears in the form of lines. The physicist Balmer had discovered that these lines follow a defined standard, and for the hydrogen atom he found the mathematical formula of the standard. However nobody knew why those lines appeared, nor why they had that distribution according to Balmer formula.


Niels Bohr who deciphered the mystery. Inhaled in the work of Planck, Bohr had the idea of applying his postulate in the hydrogen atom.

In the Bohr’s hydrogen atom model an electron gyrates about a proton, in a circular trajectory, named fundametnal status. By exciting the atom, the electron jumps to another orbit, and in this jump it emits energy (photon).


To understand the mysteries of the atom of Bohr, earlier we go to explain the concepts of centrifugal force and angular momentum.

If you are driving a car in a road with 100km/h, and see ahead a plate of dangerous curve, followed by a second a plate of maximum speed 60km/h, and you do not reduce your speed, what does happen?

The result is predictable. When making the curve, you feel that the car wants to leave the road. And perhaps you have even already passed by a situation like that, and your car really left the road.

What is it that impels the car to go off the road, when making the curve?

The force that impels an object out, when it covers a curvilinear trajectory, is vulgarly named centrifugal force. Actually this force does not exist, and it is only apparent (if had a centrifugal force acting on the Moon, this force would be cancelled by the Earth’s gravitational force, and the Moon would have to move through a rectilinear uniform movement). But for didactics effect, the concept of force centrifugal is used, because frequently it facilitates the explanation.


If you already moored a rock in the tip of a string, and keept the rock gyrating while held the other tip of the string, you already have felt the centrifugal force of the rock too, trying to make the string to scape from your hand. And you had observed that, so faster the the rock gyrates, stronger becomes the force of the string trying to leave your hand. If you turn it very fast, you dont get to hold the string, and it will scape from your hand.


Well, after understanding the centrifugal force concept, now let us see the concept of angular momentum.

Suppose that you moored a rock with mass “m? in the extremity of a spring, and is turning this rock with speed V. The angular momentum of the rock is m.V.R.

If you increase the speed V, what will happen?

The centrifugal force of the rock goes to strain the spring, and the radius of the trajectory goes to increase.

As you can increase the speed gradually, the radius can go growing slowly. That is, the radius of the trajectory can have any value. And therefore the angular momentum can have any value.

In the atom of Bohr this is forbidden. The electron can gyrate only in orbits which radius are the following: 1, 2, 4, 9, 25. So, in his theory the angular momentum of the electron is quantized, having always values that are entire multiples of the Planck’s constant h. That is, the angular momentum can have values h, 2h, 3h, 4h... only.

This quantization of the angular momentum was seen with perplexity by the physicists of that age. After all, by what reason the electron was forbidden to turn in any orbit with any radius, and with any angular momentum?


Another problem with the Bohr’s model is that according to Maxwell’s theory an electron moving in circular trajectory would have to emit radiation, to lose energy because of this, and finally this electron would have to fall down into the nucleus. To prevent this inconvenience, Bohr proposed a postulate according to which the electron can turn about the nucleus without emitting energy.


Basically, the Bohr’s model was classic in the Newtonian conception, but Bohr applied quantum concepts on it. It was therefore a hybrid, classic-quantum model.


The blow of mercy on the Bohr’s atom came with the perfectioning of the spectroscopic measurements, when was verified that the hydrogen atom emits some very thin lines, which from his model could not be explained. Moreover, his model did not succeed to explain the helium atom.


In view of the unsurmountable difficulties that the model faced, the physicists had started to look for new solutions, and finally it appeared the Schrödinger’s theory, that conceptually was totally distinct of the theory of Bohr, and was efficient in explaining the atomic phenomena where the Bohr’s model failed. And as could not leave of being, the physicists had arrived at the conclusion that the model of Bohr was incorrect.


In the theory of Schrödinger the classic concepts of the Bohr’s model had been discarded, giving place to the new concepts that had been established in the Quantum Mechanics, namely:

  • 1 - The electron left of being corpuscular, passing to be considered a probability cloud.
  • 2 - The concept of trajectory of the electron was abolished
  • 3 - The electron does not peruse the space that separates two levels of energy
  • 4 - The mechanism of emission of photons is different in the two models (we will speak about ahead)


The mistery of the Bohr´s atom

Although the failure of the Bohr’s model, however a great mystery persisted, as it is explained as follows.


The values that if one gets from the Balmer’s formula relate to the energies (photons) emitted by the hydrogen atom. To get those values with his model, Bohr considered that, in the instant when the atom emits a photon, the electron is in equilibrium due two forces: the force Fa of attraction with the proton, and the centrifugal force Fc due to speed of rotation to about the proton.

Therefore, in his model, in the instant of the emission of photons the electron is under the action of centrifugal the centrifugal force , that is, in the mechanism of emission of photons from the model of Bohr there is the performance of a centrifugal force on the electron.

In other words:
the emission mechanism depends inexorablely on the action of a centrifugal force.


Well, the model of Bohr obtained fantastic results. For example, by using his model, one calculates1 the Rydberg constant. Compare the value gotten from:

the experiments: RH = 10.967.757
the theoretical calculation: RH = 10.968.100
Impressive, isn’t?
Coincidence ?

Only if we believe that it is coincidence with the same faith with which a religious one believes miracles. Moreover, the Bohr model supplied other spectacular results. From the laws of the probability, it is impossible that it can be mere coincidence. And therefore there is something of truth in his model.

That’s why Schrödinger said:
It is difficult to believe that this result is merely an accidental mathematical consequence of the quantum conditions, and has no deeper physical meaning2.
He believed that Bohr’s successes would be consequence of unknown mechanisms, and he tried to find them.


The conclusion is that centrifugal force really plays some function in the instant when a photon is emitted by an atom.


But just here the great mystery is. The mechanism of emission of photons from the Schrödinger’s theory does not admit that one assumes that the centrifugal force plays some role in the emission of photons. The mechanism of emission of photons according to Quantum Mechanics is by resonance, a total incompatible process with the hypothesis of centrifugal force on the electron in the instant of the emission. In short, the theory of Schrödinger does not admit centrifugal force, and therefore the Bohr’s model must be completely wrong, so that the model of the Quantum Mechanics may be correct.

But we already saw that mathematically, from the laws of probability, it is impossible that the model of Bohr can be completely wrong. The centrifugal force must have some linking with the mechanism of emission of the atom, and in this in case it is lacking something in the Quantum Mechanics.

In another words:

  • a) Whereas the model of Bohr cannot be completely wrong, as they certify the laws of the probability…
  • b)… on the other hand the model of the Quantum Mechanics cannot be completely certain, because it states that the Bohr model is completely wrong.


Therefore there is here a great mystery that defies the Quantum Mechanics.

That’s why the theorists decided to state that the spectacular successes of Bohr’s theory are accidental. In a paper3 in which proposes the helical trajectory of the electron for unifying the relativity with the quantum theory, the physicist Natarajan writes, commenting the success of Bohr theory in explaining the espectra bands:

But this significant sucess along with the other spectacular successes of Bohr’s theory of the hydrogen atom is now considered by physicists as ‘accidental’ after the development of Quantum Mechanics.


But as said Schrödinger it’s hard to believe that Bohr’s successes are accidental. Actually it is impossible, from the laws of probability. It’s probable that Schrödinger started to suppose that Bohr’s successes could have connection with the electron’s zitterbewegung. Schrödinger and Heisenberg had a different view on the question of how Quantum Mechanics would have to be developed. Schrödinger would like to follow the way by considering the zitterbewegung as an electron’s helical trajectory. While Heisenberg proposed to develop Quantum Mechanics by considering that the concept of trajectory could not be kept in the theory. Such Heisenberg’s view is today known as the Interpretation of Copenhagen, and it prevailed in the development of the theory.


Believing that Bohr’s successes are accidental, the theorists believe in the inadmissible, because it’s comfortable, but actually they deceive themselves. Unlike, as Schrödinger did not accept to deceive himself, he abandoned the dispute with Heisenberg, when realized that the Theoretical Physics had followed that way preconized by the interpretation of Copenhagen. In short, it’s hard to believe that Bohr model has not a botton of truth.

End of the mistery of Bohr’s successes

As said in the PESWiki article Quantum Ring Theory 4, this new theory was developed according to the Schrödinger’s view on the zitterbewegung, interpreted as the electron’s helical trajectory

The mistery of Bohr’s successes is explained through a solution proposed in QRT, where it is proposed a new hydrogen model, with the following fundamental new proposals:

  • a) In the new hydrogen atom, the electron moves through a helical trajectory about the proton
  • b) The space of the electrosphere about the proton has dilation, due to the repulsive gravity (the same repulsive gravity that causes the expansion of the Universe, as predicted in Einstein’s theory when he proposed the cosmological constant).
  • c) This new hydrogen atom conciliates the Bohr’s hydrogen model with the Schrödinger’s equation
  • d) Actually the Schrödinger’s equation is the mathematical solution for the hydrogen atom proposed in Quantum Ring Theory

Bohr’s botton of truth

Quantum Ring Theory shows that:

  • 1- Bohr’s model is wrong. However there is a botton of truth in his model, because in spite of the emission of photons have no connection with the centripetal force, however the centripetal force on the electron exists in the instant when an atom is emitted, and the value of such force is the same of the force that the proton attracts the electron, as predicted in Bohr’s model.
  • 2- The atom model of Quantum Mechanics is correct. However it is partially wrong, because a centripetal force exists on the electron in the instant of a photon’s emission, as predicted by Bohr’s theory (Bohr made a mistake because this centripetal force has not connection with the emission of the photon, which happens by a resonance phenomenon, as correctly predicted in Quantum Mechanics.


References

1- R. Eisberg, R. Resnick, Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles, John Wiley & Sons, 1974

2- E. Schrödinger , On a Remarkable Property of the Quantum-Orbits of a Single Electron, 1922

3- T. S. Natarajan, Unified Conceptual Foundation for Relativity and Quantum Mechanics, Physics Essays, V. 9, No. 2, 1996, pg 302

4- W. Guglinski, Quantum Ring Theory – Foundations for Cold Fusion, Bäuu Press, 2006

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