The electron in a hydrogen atom spends most of its time 0.53 ×10^-10 m from the nucleus, whose r

step 1 For this question, we're told that the radius of the electron's orbit from the nucleus of an ato

The electron in a hydrogen atom spends most of its time 0.53...

The electron in a hydrogen atom spends most of its time $0.53 \times 10^{-10} \mathrm{m}$ from the nucleus, whose radius is about $0.88 \times 10^{-15} \mathrm{m} .$ If each dimension of this atom was increased by the same factor and the radius of the nucleus was increased to the size of a tennis ball, how from the nucleus would the electron be?

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Key Concepts

Hydrogen Atom Structure

This concept involves understanding the relative sizes within an atom. The electron, which is described by a probability cloud in quantum mechanics, is spread out in an orbital that is vastly larger than the nucleus. Recognizing the immense difference in scale between the electron orbitals and the nucleus is key to appreciating atomic structure.

Scaling and Proportionality

Scaling laws allow one to determine how changes in one dimension affect other dimensions when a system is uniformly enlarged. In this context, uniformly increasing the dimensions of an atom involves multiplying both the electron orbit and the nucleus by the same scaling factor, preserving their relative proportions while making their absolute sizes larger.

Orders of Magnitude

This concept deals with comparing very large or very small quantities by understanding their power-of-ten differences. The problem highlights that the atomic orbital radius is many orders of magnitude larger than the nuclear radius, and scaling the dimensions forces one to translate these differences into more familiar size comparisons.

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