The amount of meat in prehistoric diets can be determined by measuring the ratio of the isotopes nitrogen-15 to nitrogen-14 in bone from human remains. Carnivores concentrate $^{15}N$, so this ratio tells archaeologists how much meat was consumed by ancient people. Suppose you use a velocity selector to obtain singly ionized (missing one electron) nitrogen atoms of speed 8.50 km/s and bend them along a semicircle within a uniform magnetic field. The $^{14}N$ atoms travel along a semicircle with a diameter of 27.7 cm. The measured masses of these isotopes are $2.32 \times 10^{-26}$ kg ($^{14}N$) and $2.49 \times 10^{-26}$ kg ($^{15}N$).
Find the separation of the $^{14}N$ and $^{15}N$ isotopes at the detector.
Express your answer with the appropriate units.
s = 3.16 cm
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