In the Bohr model for hydrogen, the radius of the nth orbit can be shown to be n² times the radius of the first Bohr orbit r₁ = 0.05 nm. Similarly, the energy of an electron in the nth orbit is 1/n² times its energy when in the n = 1 orbit. What is the circumference of the n = 100 orbit? (This is the distance the electron has traveled after having revolved around the proton once.) For such large-n states, the orbital frequency is about equal to the frequency of the photon emitted in a transition from the nth level to an adjacent level with n + 1 or n - 1. Given this, find the frequency and corresponding period of the electron’s orbit by computing the frequency associated with the transition from n = 100 to n = 101. Using your values for the electron’s orbital size (distance) and travel time (period), calculate the approximate speed of the electron in the 100th orbit. How does this speed compare to the speed of light?