In defining the sizes of orbitals, why must we use an arbitrary value, such as 90 % of the proba

step 1 So we're being asked, why is it that when we're defining an orbital size that we Onley use like

In defining the sizes of orbitals, why must we use an...

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Key Concepts

Quantum Mechanical Nature of Orbitals

Orbitals in quantum mechanics are not solid regions with fixed boundaries but rather mathematical functions (wave functions) that describe the probability of finding an electron in a given region of space. This probabilistic description means that an electron does not have a well-defined edge, leading to the need for a convention when describing the 'size' of an orbital.

Probability Density and Wave Functions

The probability density, derived from the square of the wave function, informs us about how likely it is to find an electron at a particular point in space. This density decreases gradually rather than dropping to zero at a specific boundary, indicating that the electron's location is inherently spread out over an infinite space.

Arbitrary Thresholds in Orbital Definitions

Because the probability density of an electron fades out gradually, scientists need to define an arbitrary cutoff—often a percentage threshold like 90%—to describe a practical boundary for an orbital. This cutoff is a convention used to provide a useful, albeit imprecise, estimation of orbital size and shape for visualization and comparison purposes.

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