Two isotopes of carbon, carbon-12 and carbon-13, have masses of 19.93x10^-27 kg and 21.59x10^-27 kg, respectively. These two isotopes are singly ionized (+e) and each is given a speed of 6.667x10^5 m/s. The ions then enter the bending region of a mass spectrometer where the magnetic field is 0.8500T. Determine the spatial separation between the two isotopes after they have traveled through a half circle.
r = mv / (eB)
m = (er^2/2V)*B^2
The Attempt at a Solution
In this problem, I attempted to plug in the values I knew (B, e, v and m) in order to find the radius of each individual isotope. Then i attempted to obtain the difference in radius to obtain the spatial separation between the two isotopes, however I can't seem to obtain the right answer. I'm not really sure how else to approach this problem. Perhaps I am having trouble understanding what exactly they mean by "spatial separation." I was hoping someone could clarify what I'm doing wrong and how I should be approaching this problem differently. Below are my calculations:
r1 = (19.93x10^-27) * (6.667*10^5) / (1.6x10^-19 * 0.85)
r2 = (21.59*10^-27) * (6.667*10^5) / (1.6x10^-19 * 0.85)
r2 - r1 = spatial separation (?)
Correct answer for this problem: 1.6x10^-2 m.
Someone please shed some light on this problem. Thank you!