Exercise 27.33 Part A The amount of meat in prehistoric diets can be determined

Question

Exercise 27.33 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 2.29 × 10 26 kg (14N) and 2.45 x 10 26 kg (I5N) Find the separation of the 14N and 15N isotopes at the detector Express your answer with the appropriate units Vaue Units Submit My Answers Give Up Incorrect, Iry Again, 2 attempts remaining Continue Figure 1 S1 Velocity selector selects particles with speed v. Particle detector S3 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 = mv²/(Bq)

For the N14 particle:

r = (2.45×1026) x 513000² /(0.510 x 1.6x10-19) = 79,015.20221m

For the N15 particle:

r = (2.29×1026) x 513000² /(0.510 x 1.6x10-19) = 73,855.02574m

The separation is the difference in diameters which is

2r - 2r = 2(r - r)

= -10,320.35m

If only magnitude is considered, the separation

= 10,320.35m

Related Questions

Navigate

• Browse (All)
• Browse E
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.