The amount of meat in prehistoric diets can be determined by measuring the ratio

Question

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 15N, 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 8.65 km/s and bend them along a semicircle within a uniform magnetic field. The 14N atoms travel along a semicircle with a diameter of 21.0 cm . The measured masses of these isotopes are 2.32×1026 kg (14N) and 2.49×1026 kg for (15N).

Find the separation of the 14N and 15N isotopes at the detector.

s= _____cm

Explanation / Answer

For the circular motion, the centripetal force (mv²/r) is the magnetic force (Bqv) so:
mv²/r = Bqv
B = mv/(rq)

For the N14 particle:
r = 10.5 cm = 0.105 m

Now

B = mv/(q*r1) = (2.32*10^-26*8650)/(1.6*10^-19*0.105) = 0.012 T

For the N15 particle:
r = mv/qB = (2.49×10^26 x 8650)/(0.012 x 1.6x10^-19) = 0.112 m

The separation is the difference in diameters which is
2r - 2r = 2(r - r) = 2(0.112 – 0.105) = 0.014 m = 1.4 cm

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