Question

In defining the sizes of orbitals, why must we use an arbitrary value, such as 90% of the probability of finding an electron in that region?

Short answer

An electron can’t have a distinct location but its orbital can be defined as the region of space around the nucleus where the probability of finding an electron exceeds some arbitrary value, such as 90%.

Step-by-step solution

Discuss the concept of Heisenberg’s Uncertainty Principle:

It states that it is impossible to measure simultaneously the exact position and exact momentum of a body as small as an electron.

$∆x.∆p⩾h/4\mathrm{\pi }$

or, $∆x.∆mv⩾\raisebox{1ex}{$h$}\!\left/ \!\raisebox{-1ex}{$4\mathrm{\pi }$}\right.$

Electrons can’t have a distinct location because of Heisenberg’s Uncertainty principle.

Explain the concept of fuzzy boundaries:

Schrodinger developed an equation to calculate the probability of an electron being in any given space near the nucleus. He called the regions where electrons are most likely to be found as orbitals. Each orbital around the nucleus resembles a fuzzy cloud around the nucleus or we can say that orbitals have fuzzy boundaries. The boundaries show 90% electron presence probability because the exact location can’t be pinpointed.