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 (Figure 1) to obtain singly ionized (missing one electron) atoms of speed 513km/s and want to bend them within a uniform magnetic field of 0.510T. The measured masses of these isotopes are 2.34×1026kg (14N) and 2.47×1026kg (15N).

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

Explanation / Answer

Force on object moving perpendicular to magnetic field,

F=qvB.

The Lorentz magnetic force supplies the centripetal force, so these terms are equal:

qvB=mv2/r

solving for r yields

r=mv/(qB)   

For 14N

r = 2.34×1026kg *513000m/s /(0.510T* 1.6*10-19C)

= 0.14711 m= 14.711 cm

For 15N

r = 2.47×1026kg *513000m/s /(0.510T* 1.6*10-19C)

=0.15528m = 15.528 cm

separation =2*( 15.528 cm- 14.711 cm) = 1.634 cm ANSWER

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