Answer
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In defining the sizes of orbitals, we use an arbitrary value, such as 90% of the probability of finding an electron in that region, because the concept of an orbital is based on the probability distribution of finding an electron in a particular region around the nucleus.
According to the quantum mechanical model of the atom, electrons do not follow fixed paths like planets around the sun. Instead, they are described by wave functions, which give the probability of finding an electron at a particular location. The square of the wave function, known as the electron density, represents the probability density of finding an electron at a given point in space.
The shape and size of an orbital are determined by the wave function and its associated probability density. However, the wave function extends to infinity, so it is not possible to define a precise boundary for an orbital. Instead, we use an arbitrary value, such as 90% of the probability, to define the size of an orbital.
By choosing a specific probability value, we can define a region in space where the electron is most likely to be found. The chosen value of 90% is a common convention, but other values can also be used depending on the context. This arbitrary value allows us to compare and describe the sizes of different orbitals within an atom or across different atoms.
It is important to note that the concept of an orbital and its size is a probabilistic description based on the behavior of electrons in atoms. The actual position of an electron within an orbital cannot be precisely determined, but the probability of finding it in a specific region can be calculated using the wave function.
We use an arbitrary value such as 90% because an orbital’s probability density extends to infinity — there is no natural boundary. The 90% region gives a practical, consistent way to define and compare the effective size of orbitals.
