At higher orbit, the radius of the helical path is smaller,
\(r_{p1}\lt r_{p2}\)
This is as if the orbit is a spring coil that when stretched the helical radius collapses to smaller values. Furthermoe from the post "I know where the \(2\pi\) factor is from", where the particles are at light speed in circular motion,
\(c=r\omega=r_p2\pi f_p\)
So,
\(r_p\propto\cfrac{1}{f_p}\) and so,
\(f_{p1}\gt f_{p2}\)
Frequency at higher orbit is higher than at lower orbit. This would then be consistent with the observation that the higher orbit electrons display more complex interference pattern. At lower orbit, lower frequency (higher \(\lambda\)) results in a single bright spot in the middle of two electrons in parallel orbits due to constructive interference and dark bands at low value of \(\theta_D\) on both sides of the singular bright spot, due to destructive interference.
What about the other patterns?
