The amount of meat in prehistoric diets can be determined by

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).

Solution

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