Problem: 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 2.35×10-26 kg (14N) and 2.45×10-26 kg (15N).Find the separation of the 14N and 15N isotopes at the detector.Express your answer with the appropriate units.s = ___

🤓 Based on our data, we think this question is relevant for Professor Nejad's class at YU.

FREE Expert Solution

Magnetic force must be equal to the centripetal force.

Therefore,

mv2r=qvBmvr=qB

Solving for r:

r=mvqB

For N - 14, 

rN-14 = (2.35×10-26)(513×103)/(1.6 × 10-19)(0.510) = 0.1477 m

Distance, d14 = 2r14 = (2)(0.1477) = 0.2954  m

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Problem Details

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 2.35×10-26 kg (14N) and 2.45×10-26 kg (15N).

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

Express your answer with the appropriate units.

s = ___

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Based on our data, we think this problem is relevant for Professor Nejad's class at YU.