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.
A)514
B)51
C)16
D)264,650

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. The formula is $ r_n = n^2 \times r_1 $, where $ r_1 $ is the radius of the ground state. Solving for n when $ r_n = 14 \mu m = 14000 nm $ and $ r_1 = 0.0529 nm $, we find $ n \approx 514 $.

A Hydrogen Atom with a Barely Bound Electron May Have 14μm14 \mu \mathrm { m }14μm

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