What is the ratio of the Bohr orbital radius for hydrogen in the n = 3 state to that in the n = 1 state?
A) 1/3
B) 3
C) 6
D) 9
E) 18

Question

Quizplus · Accepted Answer

The Bohr model gives the radius of the nth orbit as r_n = (a_0)n^2/Z, where a_0 is the Bohr radius for hydrogen (0.529 Å) and Z is the atomic number. Therefore, the Bohr radius for hydrogen in the n = 3 state is r_3 = (0.529 Å) x 3^2 = 4.77 Å, and the Bohr radius for hydrogen in the n = 1 state is r_1 = (0.529 Å) x 1^2 = 0.529 Å. The ratio of these radii is therefore r_3/r_1 = 4.77 Å/0.529 Å = 9, which corresponds to answer choice D.

What Is the Ratio of the Bohr Orbital Radius for Hydrogen