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 2.32×10−26 kg (14N) and 2.49×10−26 kg for (15N). Find the separation of the N14 and the N15 isotopes at the detector.

Answer 1

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