Why does the quantum mechanical description

This quantum uncertainty principle can also be expressed in terms of other variables. For example, a particle with a definitely measured energy has a fundamental limit to how precisely one can specify how long it will have that energy. Quantum indeterminacy is the assertion that the state of a system does not determine a unique collection of values for all its measurable properties. In quantum mechanical formalism, it is impossible that, for a given quantum state, each one of these measurable properties observables has a determinate sharp value.

The values of an observable will be obtained non-deterministically in accordance with a probability distribution uniquely determined by the system state. The state is destroyed by measurement, so each measured value in a collection must be obtained using a freshly prepared state. In the classical sense, these are known and repeatable.

A bullet propelled from a gun at a consistent velocity under identical conditions will always follow the same trajectory and hit the same target. In the world of quantum phenomena, this is not the case. Since either its present position or velocity is unknown, we cannot know where it will be with any certainty after a known time interval. This is called indeterminacy. We do know where it could be. Based on numerous observations, the quantum state, and the wave equation for the electron, we can determine a statistical map of probable positions for the electron.

This is called a probability distribution map, a statistical representation of the probable locations of electrons as they exist in an atom. The clouds of probability are the locations of electrons as determined by making repeated measurements—each measurement finds the electron in a definite location, with a greater chance of finding the electron in some places rather than others.

With repeated measurements, a pattern of probability emerges. The clouds of probability do not look like nor do they correspond to classical orbits. The uncertainty principle prevents us from knowing how the electron gets from one place to another, and so an orbit really does not exist as such. Nature on a small scale is much different from that on the large scale.

Probability density of hydrogen electrons : As indicated by the quantum numbers n, l, ml , this figure depicts probability clouds for the electron in the ground state and several excited states of hydrogen. While the work of Bohr and de Broglie clearly established that electrons take on different discrete energy levels that are related to the atomic radius, their model was a relatively simplistic spherical view.

This was in contrast to previous work that focused on one-electron atoms such as hydrogen. The question of how many quantum numbers are needed to describe any given system has no universal answer; for each system, one must find the answer by performing a full analysis of the system.

Formally, the dynamics of any quantum system are described by a quantum Hamiltonian H applied to the wave equation. There is one quantum number of the system corresponding to the energy—the eigenvalue of the Hamiltonian. There is also one quantum number for each operator O that commutes with the Hamiltonian i. Note that the operators defining the quantum numbers should be independent of each other. Often there is more than one way to choose a set of independent operators; so in different situations, different sets of quantum numbers may be used for the description of the same system.

The most prominent system of nomenclature spawned from the molecular orbital theory of Friedrich Hund and Robert S. Mulliken, which incorporates Bohr energy levels as well as observations about electron spin. It is also the common nomenclature in the classical description of nuclear particle states e.

Quantum numbers : These four quantum numbers are used to describe the probable location of an electron in an atom. The first quantum number describes the electron shell, or energy level, of an atom. The value of n ranges from 1 to the shell containing the outermost electron of that atom. For example, in caesium Cs , the outermost valence electron is in the shell with energy level 6, so an electron in caesium can have an n value from 1 to 6.

This number therefore has a dependence only on the distance between the electron and the nucleus i. The average distance increases with n , thus quantum states with different principal quantum numbers are said to belong to different shells.

The second quantum number, known as the angular or orbital quantum number, describes the subshell and gives the magnitude of the orbital angular momentum through the relation.

In chemistry, this quantum number is very important since it specifies the shape of an atomic orbital and strongly influences chemical bonds and bond angles. The magnetic quantum number describes the energy levels available within a subshell and yields the projection of the orbital angular momentum along a specified axis. The fourth quantum number describes the spin intrinsic angular momentum of the electron within that orbital and gives the projection of the spin angular momentum s along the specified axis.

Each electron in any individual orbital must have different spins because of the Pauli exclusion principle, therefore an orbital never contains more than two electrons. For example, the quantum numbers of electrons from a magnesium atom are listed below. Remember that each list of numbers corresponds to n , l , m l , m s.

Table relating quantum numbers to orbital shape : The relationship between three of the four quantum numbers to the orbital shape of simple electronic configuration atoms up through radium Ra, atomic number The fourth quantum number, the spin, is a property of individual electrons within a particular orbital. Each orbital may hold up to two electrons with opposite spin directions. Illustrate how the Pauli exclusion principle partially explains the electron shell structure of atoms.

The Pauli exclusion principle, formulated by Austrian physicist Wolfgang Pauli in , states that no two fermions of the same kind may simultaneously occupy the same quantum state. More technically, it states that the total wave function for two identical fermions is antisymmetric with respect to exchange of the particles.

The Pauli exclusion principle governs the behavior of all fermions particles with half-integer spin , while bosons particles with integer spin are not subject to it.

Fermions include elementary particles such as quarks the constituent particles of protons and neutrons , electrons and neutrinos. In addition, protons and neutrons subatomic particles composed from three quarks and some atoms are fermions and are therefore also subject to the Pauli exclusion principle. As such, the Pauli exclusion principle underpins many properties of everyday matter from large-scale stability to the chemical behavior of atoms including their visibility in NMR spectroscopy.

In the theory of quantum mechanics, fermions are described by antisymmetric states. Through spectroscopy one could see the subtle patterns of light excited atoms emitted, but a precise explanation for their being eluded scientists. Niels Bohr was the first to suggest something akin to our modern theory of quantum mechanics.

In Bohr's model , an atom's electrons circled the nucleus, much like planets orbit the sun, but were restricted to only a few specific energies. The transitions between these restricted orbits accounted for the emission and absorption lines of elements. However, this quantization was not justified, and though empirically sound, proved unsatisfactory.

It was not until Erwin Schrodinger introduced his wave equation that the quantized nature of the atom was fully understood. The visible spectrum of hydrogen, with its characteristic distinct lines. Thicker lines indicate a greater number of available transitions - the hyper-fine structure.

Although Schrodinger's equation is inherently non-relativistic and many improvements have been made to his original theory, it still is a powerful predictive and pedagogical tool. According to quantum mechanical theory, all the measurable properties of a particle can be calculated from its wave function , whose evolution is dictated by the equation.

In this new theory, probabilistic solutions supersede the determinism of classical mechanics. The solutions to this equation can only be used to determine a probability distribution for the measurables of a particle, position, momentum, etc. Hence unlike planetary orbits, electrons bound by a nucleus take on a much fuzzier, cloud-like existence, first called orbitals by Mulliken.

Even the closest and most tightly bound electron in a hydrogen atom may be, however unlikely, thousands of miles away. This implausible, but very real physical result highlights the probabilistic nature of the solutions. Atomic orbitals are described by three parameters n, l, and m, called quantum numbers.

These correspond to the state of the electron in question. Additionally, the Dirac equation, a revised version of Schrodinger's equation which incorporates relativity, adds a fourth quantum number, s , the spin quantum number.

They obey the following relationships:. Podolsky, and N. Rosen Phys. Abstract In a complete theory there is an element corresponding to each element of reality.

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