A hydrogen atom with a barely bound electron may have an average radius as large as a bacterium, which is a radius of $14 \mu \mathrm { m } .$ What is the nearest principal quantum number of the atom in this state? The radius for ground state hydrogen is 0.0529 nm.

Question

Quizplus · Accepted Answer

The radius of a hydrogen atom in a given state is proportional to the square of the principal quantum number, $ n^2 $. Given that the radius of the ground state is 0.0529 nm, we can set up the equation $(n^2 \times 0.0529 \text{ nm}) = 14 \times 10^3 \text{ nm}$. Solving for $ n $, we find $ n \approx 514 $.

A Hydrogen Atom with a Barely Bound Electron May Have 14μm.14 \mu \mathrm { m } .14μm.

A Hydrogen Atom with a Barely Bound Electron May Have $14 \mu \mathrm { m } .$