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^2 $. Given that the radius in the ground state is 0.0529 nm, we can set up the equation $ n^2 \times 0.0529 \, \text{nm} = 14 \, \mu\text{m} $. Converting $ 14 \, \mu\text{m} $ to nm gives $ 14,000 \, \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 $14 \mu \mathrm { m } .$