# Heisenberg atomic model: characteristics and limitations

The **atomic model Heisenberg** (1927) introduced the uncertainty principle into the electron orbitals surrounding the atomic nucleus. The leading German physicist laid the foundations of quantum mechanics to estimate the behavior of the subatomic particles that make up an atom.

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

In summary, it is not possible to predict the value of both variables simultaneously. The foregoing does not imply that any of the aforementioned magnitudes cannot be precisely known. Whenever separated, there is no impediment to obtaining the value of the interest.

However, uncertainty occurs when it comes to knowing simultaneously two conjugate magnitudes, such as position and linear momentum, and time together with energy.

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

**Characteristics**

In March 1927, Heisenberg published his work *on the perceptual content of kinematics and theoretical quantum 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 appears as an explanation that complements the new atomic theories about the behavior of electrons. Despite using measuring instruments with high precision and sensitivity, indeterminacy remains present in any experimental test.

– Due to the uncertainty principle, when analyzing two related variables, if you have an accurate knowledge of one of them, the uncertainty about the value of the other variable will increase.

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

– The relationship between the two variables is given by an inequality. According to Heisenberg, the product variations of momentum and particle position are always greater than the ratio of Planck’s constant (6.62606957 (29) x 10 ^{-34} Jules x seconds) and 4n as detailed in the following mathematical expression:

The caption corresponding to this expression is as follows:

∆p: indeterminacy of linear momentum.

:X: position indeterminacy.

h: Constant plank.

π: pi number 3.14.

– Given the above, the product of the uncertainties has the relation h / 4π as its lower limit, 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 conjugated canonical quantities. For example, the Heisenberg uncertainty principle is perfectly applicable to the energy-time pair, as detailed below:

In this expression:

∆E: energy indeterminacy.

:T: time indeterminacy.

h: Constant plank.

π: pi number 3.14.

– It results from this model that absolute causal determinism in the canonical conjugate variables is impossible, because to establish this relationship it is necessary to have knowledge about the initial values of the variables in the study.

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

**experimental tests**

Heisenberg’s 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 the time suggested that the variables linear momentum, position, angular momentum, time, energy, among others, for subatomic particles were operationally defined.

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

The above implies the definition of a reference system for measurements, the measuring instrument and the method of use of said instrument, in accordance with the scientific method.

Accordingly, the variables described by the subatomic particles must behave deterministically. That is, their behavior had to be accurately and precisely predicted.

However, each time a test of this nature was performed, 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 question of measuring the velocity 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 intrinsic velocity and position of the electron, whereby the object of measurement is altered by experimental conditions.

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

**Quantum Mechanics Except Classic Mechanics**

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

Consequently, it is assumed that accurate knowledge of measurements at the subatomic level is limited by the thin line separating classical and quantum mechanics.

**limitations**

Despite explaining the indeterminacy of subatomic particles and establishing the differences between classical and quantum mechanics, the Heisenberg 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 canonical conjugate variables is indeterminate. Consequently, the uncertainty inherent in subatomic processes is significant.