In the Bohr Model of the hydrogen atom,what is the ratio of the speed of the electron moving in the n = 2 orbit divided by the speed of the electron in the n = 3 orbit?
A)0.66
B)1.5
C)2.25
D)0.44
E)its speed is independent of n

Question

Quizplus · Accepted Answer

According to Bohr's Model, the electron speed is inversely proportional to the square of the orbit radius (v ∝ 1/r^2). Thus, we can calculate the ratio of speeds as (v2/v3) = (r3/r2)^2. From the formula for the radius of Bohr's orbits, we have r ∝ n^2, and therefore, (r3/r2)^2 = (3/2)^2 = 2.25. Hence, v2/v3 = 1/2.25 = 0.444 ~ 0.66 (rounded to two decimal places). Thus, the correct choice is B.

In the Bohr Model of the Hydrogen Atom,what Is the Ratio