One method for determining the amount of corn in early Native American diets is

Question

One method for determining the amount of corn in early Native American diets is the stable isotope ratio analysis (SIRA) technique. As corn photosynthesizes, it concentrates the isotope carbon-13, whereas most other plants concentrate carbon-12. Overreliance on corn consumption can then be correlated with certain diseases, because corn lacks the essential amino acid lysine. Archaeologists use the mass spectrometer to separate the 12C and 13C isotopes in samples of human remains. Suppose you use a velocity selector to obtain singly ionized (missing one electron) atoms of speed 8.45km/s and want to bend them within a uniform magnetic field in a semicircle of diameter 25.3cm for the 12C. The measured masses of these isotopes are 1.99

Explanation / Answer

q = charge = 1.6 x 10-19 C

m1 = mass of 12C = 1.99 x 10-26 kg

m2 = mass of 13C = 2.16 x 10-26 kg

d1 = diameter of 12 C = 25.3 cm = 0.253 m

r1 = radius of 12 C = 25.3 cm/2 = 0.1265 m

V = speed = 8.45 km/s = 8.45 x 103 m/s

A)

the radius of C-12 is given as ::

r1 = m1 V/qB

B = m1 V/qr1

B = (1.99 x 10-26 )(8.45 x 103 ) / (1.6 x 10-19 x 0.1265)

B = 0.00831

B)

Diameter of 13C can be given as ::

r2 = m2 V/qB

inserting the values

r2 = (2.16 x 10-26 )(8.45 x 103 )/(1.6 x 10-19 x 0.00831)

r2 = 0.1373 m

C )

separation at the detector is given as ::

separation = r2 - r1 = 0.1373 - 0.1265 = 0.0108 m

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