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 8.95 km/s and bend them along a semicircle within a uniform magnetic field. The 14N atoms travel along a semicircle with a diameter of 24.5 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 N14 and the N15 isotopes at the detector.

Explanation / Answer

Magnetic force on charged particle must be equal to the centripetal force

mv^2 / r = qvB

mv/r = qB

r = mv/qB

For C-12 :-

rC-12 = mc-12v / qB ..........(1)

for N-14 :-

rN-14 = mrN-14v / qB ..........(2)

for N-15 :-

rN-15 = mrN-15v / qB ..........(3)

divide (1) by (2)

rC-12 / rN-14 = [mc-12v / qB ] / [mrN-14v / qB]

rC-12 / rN-14 = mC-12 / mN-14

rN-14 = (mN-14 / mC-12)*rC-12

rN-14 = (2.32 x 10^-26 / 1.99 x 10^-26)*(24.5 x 10^-2 m)

rN-14 = 0.2856 m

divide (1) by (3)

rC-12 / rN-15 = [mc-12v / qB ] / [mrN-15v / qB]

rC-12 / rN-15 = mC-12 / mN-15

rN-15 = (mN-15 / mC-12)*rC-12

rN-15 = (2.49 x 10^-26 / 1.99 x 10^-26)*(24.5 x 10^-2 m)

rN-15 = 0.3066 m

Therefore, separation between isotopes is

Delta(r) = rN-15 - rN-14

Delta(r) = 0.3066 m - 0.2856 m

Delta(r) = 0.021 m

Delta(r) = 2.10 cm

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