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

step 1 All right, guys, from A2 of Chapter 7. So in defining the size of the orbitals, why must we use

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

Key Concepts

Arbitrary Probability Thresholds

Because the electron probability density extends infinitely, any boundary chosen to define the size of an orbital is inherently arbitrary. Selecting a threshold, such as 90% of the total probability, is a practical decision that encapsulates the majority of the electron’s probability without requiring an impossible, all-encompassing limit. This arbitrary cutoff is useful for making comparisons and calculations while acknowledging the probabilistic nature of electron positions.

Quantum Mechanics in Atomic Structure

In quantum mechanics, electrons are not confined to precise orbits or boundaries; instead, they are described by wavefunctions that provide a probability distribution of where an electron might be found. This fundamental concept underlies the nature of atomic orbitals and explains why their definitions rely on probabilities rather than fixed spatial limits.

Electron Probability Distribution

The electron in an atom exists in a state of probability, with its position described by a mathematical function that decreases gradually but never truly reaches zero. This distribution means that while the largest likelihood of finding an electron is near the nucleus, there is still a nonzero chance of finding it far from the nucleus, making it necessary to choose a cutoff value to define a practical 'size' for an orbital.

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