In the Bohr model for hydrogen, the radius of the nth orbit can beshown to be n2 times

Chapter 10, Problem Challenges 5

(choose chapter or problem)

In the Bohr model for hydrogen, the radius of the nth orbit can beshown to be n2 times the radius of the first Bohr orbit r1 0.05 nm(see Example 10.3). Similarly, the energy of an electron in the nthorbit is times its energy when in the n 1 orbit. What is thecircumference of the n 100 orbit? (This is the distance the elec-tron has traveled after having revolved around the proton once.)For such large-n states, the orbital frequency is about equal to thefrequency of the photon emitted in a transition from the nth levelto an adjacent level with n 1 or n 1. Given this, find the fre-quency and corresponding period of the electrons orbit by com-puting the frequency associated with the transition from n 100 ton 101. Using your values for the electrons orbital size (distance)and travel time (period), calculate the approximate speed of theelectron in the 100th orbit. How does this speed compare to thespeed of light?