Exercise 27.33 21 of 25 stant Part A The amount of meat in prehistoric diets can

Question

Exercise 27.33 21 of 25 stant Part A 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 (Figure 1) to obtain singly ionized (missing one electron) atoms of speed 513 km/s and want to bend them within a uniform magnetic field of 0.510 T. The measured masses of these isotopes are 2.34 x10 26 kg (14N) and 2.48 x 10 26 kg (15N). Find the separation of the 14N and 15N isotopes at the detector Express your answer with the appropriate units. alue Units Submit Provide Feedback Next > Figure 1 of1 > Si Velocity selector selects particles with speed v EB Particle detector RI Magnetic field separates particles by mass; the greater a particle's mass, the larger is B the radius of its path.

Explanation / Answer

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

mv²/r = Bqv

r = mv/(Bq)

For the N15 particle:

r? = (2.48×10?26) x 513000 /(0.510 x 1.6x10-19) = 0.1559m

For the N14 particle:

r? = (2.34×10?26) x 513000 /(0.510 x 1.6x10-19) = 0.1471m

The separation is the difference in diameters which is

2r? - 2r? = 2(r1 – r2) = 0.017579m (or 1.7579cm)

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