**What is the Heisenberg atomic model?**

He **Heisenberg’s atomic model** (1927) introduces the uncertainty principle in the electron orbitals surrounding the atomic nucleus. The prominent German physicist established the foundations of quantum mechanics to estimate the behavior of the subatomic particles that make up an atom.

Werner Heisenberg’s uncertainty principle states that it is not possible to know with certainty the position and momentum of an electron at the same time. The same principle applies to the variables time and energy; that is, if we have an indication about the position of the electron, we will not know the linear momentum of the electron, and vice versa.

In short, it is not possible to simultaneously predict the value of both variables. This does not imply that any of the previously mentioned magnitudes cannot be known with precision. As long as it is separate, there is no impediment to obtaining the interest value.

However, uncertainty occurs when it is a question of simultaneously knowing two conjugated magnitudes, as is the case of position and linear momentum, and of time together with energy.

This principle arises due to a strictly theoretical reasoning, as the only viable explanation to give reason for scientific observations.

**Characteristics of the Heisenberg atomic model**

In March 1927 Heisenberg published his work *On the perceptual content of quantum theoretical kinematics and mechanics*where he detailed the principle of uncertainty or indeterminacy.

This principle, fundamental in the atomic model proposed by Heisenberg, is characterized by the following:

The uncertainty principle emerges as an explanation that complements the new atomic theories about the behavior of electrons. Despite using measuring instruments with high precision and sensitivity, uncertainty is still present in any experimental test.

Because of the uncertainty principle, when analyzing two related variables, if there is accurate knowledge of one of them, then the uncertainty about the value of the other variable will be greater each time.

The momentum and the position of an electron, or other subatomic particle, cannot be measured at the same time.

The relationship between both variables is given by an inequality. According to Heisenberg, the product of the variations of the linear momentum and the position of the particle is always greater than the quotient between Plank’s constant (6.62606957(29) ×10 -34 Jules x seconds) and 4π, as detailed in the following mathematical expression:

The legend corresponding to this expression is as follows:

∆p: indeterminacy of the linear momentum.

∆x: indeterminacy of the position.

h: Planck’s constant.

π: pi number 3.14.

In view of the above, the product of the uncertainties has as its lower limit the ratio h/4π, which is a constant value. Therefore, if one of the magnitudes tends to zero, the other must increase in the same proportion.

This relationship is valid for all pairs of conjugate canonical quantities. For example: Heisenberg’s uncertainty principle is perfectly applicable to the energy-time pair, as detailed below:

In this expression:

∆E: indeterminacy of energy.

∆t: indeterminacy of time.

h: Planck’s constant.

π: pi number 3.14.

From this model it can be deduced that absolute causal determinism in conjugate canonical variables is impossible, since to establish this relationship one should have knowledge of the initial values of the study variables.

Consequently, the Heisenberg model is based on probabilistic formulations, due to the randomness that exists between the variables at subatomic levels.

**experimental tests**

The Heisenberg uncertainty principle emerges as the only possible explanation for the experimental tests that took place during the first three decades of the 21st century.

Before Heisenberg enunciated the uncertainty principle, the precepts in force at that time suggested that the variables linear momentum, position, angular momentum, time, energy, among others, for subatomic particles were defined operationally.

This meant that they were treated as if it were classical physics; that is, an initial value was measured and the final value was estimated according to the pre-established procedure.

The foregoing implied defining a reference system for measurements, the measuring instrument and the way of using said instrument, in accordance with the scientific method.

According to this, the variables described by subatomic particles should behave in a deterministic way. That is, its behavior had to be accurately and precisely predicted.

However, every time a test of this nature was carried out, it was impossible to obtain the theoretically estimated value in the measurement.

The measurements were distorted due to the natural conditions of the experiment, and the result obtained was not useful to enrich the atomic theory.

**Example**

For example: if it is a matter of measuring the speed and position of an electron, the setup of the experiment must contemplate the collision of a photon of light with the electron.

This collision induces a variation in the velocity and the intrinsic position of the electron, with which the object of the measurement is altered by the experimental conditions.

Therefore, the researcher encourages the occurrence of an inevitable experimental error, despite the accuracy and precision of the instruments used.

**Quantum mechanics other than classical mechanics**

In addition to the above, Heisenberg’s uncertainty principle states that, by definition, quantum mechanics works differently from classical mechanics.

Consequently, it is assumed that precise knowledge of measurements at the subatomic level is limited by the fine line between classical and quantum mechanics.

**Limitations of the Heisenberg model**

Despite explaining the indeterminacy of subatomic particles and establishing the differences between classical and quantum mechanics, Heisenberg’s atomic model does not establish a single equation to explain the randomness of this type of phenomenon.

Furthermore, the fact that the relationship is established through an inequality implies that the range of possibilities for the product of two conjugate canonical variables is indeterminate. Consequently, the uncertainty inherent in subatomic processes is significant.

**Articles of interest**

Schrödinger’s atomic model.

Broglie’s atomic model.

Chadwick’s atomic model.

Perrin’s atomic model.

Thomson’s atomic model.

Dalton’s atomic model.

Dirac Jordan’s atomic model.

Democritus’s atomic model.

Leucippus’ atomic model.

Bohr’s atomic model.

Sommerfeld’s atomic model.

Current atomic model.

**References**

Beyler, R. (1998). Werner Heisenberg. Encyclopædia Britannica, Inc. Retrieved from: britannica.com

The Heisenberg Uncertainty Principle (nd). Recovered from: hiru.eus

Garcia, J. (2012). Heisenberg’s uncertainty principle. Retrieved from: hiberus.com

Atomic models (nd). National Autonomous University of Mexico. Mexico DF, Mexico. Retrieved from: asesorias.cuautitlan2.unam.mx

Werner Heisenberg (sf). Retrieved from: the-history-of-the-atom.wikispaces.com

Wikipedia, The Free Encyclopedia (2018). Planck’s constant. Retrieved from: es.wikipedia.org

Wikipedia, The Free Encyclopedia (2018). Heisenberg’s uncertainty relation. Retrieved from: es.wikipedia.org