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 15 N, 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) 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 2.30 times 10^-26 kg (14N) and 2.50 times 10^-26 kg (15N).

Explanation / Answer

Speed of electron v = 513 km/ s= 513 x10 3 m/s

Magnetic field B = 0.51 T

Mass of 14 N is m = 2.3 x10 -26 kg

Mass of 15 N is m ' = 2.5 x10 -26 kg

Charge of ion q = 1.6 x10 -19 C

In magnetic filed ,Bvq = mv 2/ r

                           Bq = mv/r

From this radius r = mv /Bq

radius of 14 N is r = mv / Bq

                           = (2.3 x10 -26)(513 x10 3) /(0.51)(1.6x10 -19 )

                           = 0.14459 m

radius of 15 N is r ' = m 'v / Bq

                           = (2.5 x10 -26)(513 x10 3) /(0.51)(1.6x10 -19 )

                           = 0.15716 m

Required separation = 2r ' - 2 r

                              = 2(r ' - r)

                              = 2(0.15716 -0.14459)

                              = 0.02515 m

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