One method for determining the amount of corn in early Native American di-ets is

Question

One method for determining the amount of corn in early Native American di-ets is the stable isotope ratio analysis (SIRA) technique. As corn photosynthe-sizes, it concentrates the isotope carbon-13, whereas most other plants concen-trate carbon-12. Overreliance on corn consumption can then be correlated with certain diseas-es, because corn lacks the essential amino acid lysine. Archaeologists use a mass spectrometer to separate the 12C and 13C isotopes in samples of humans remains. Suppose you use a velocity selector to obtain single ionized (missing one electron) atoms of speed 8.50 km/s and want to bend them within a uniform magnetic field in a semicircle of diameter 25.0 cm for the 12C. The measured masses of these isotopes are 1.99 x 10-26 kg (12C) and 2.16 x 10-26 kg (13C). (a) What strength of magnetic field is required? (b) What is the diameter of the 13C semicircle? (c) What is the separation of the 12C and 13C ions at the detector at the end of the semicircle? Is this dis-tance large enough to be easily observed?

Explanation / Answer

(a)

B = mv/qr

Mass of 12C = 1.99 x 10-26 kg

v = 8500 m/s

r = 0.125 m

q = 1.6*(10^ -19) C

B = 8.46*(10^ -3)

(b) B = mv/qr

r = mv/qB

Mass of 13C = 2.16 x 10-26 kg

v = 8500 m/s

q = 1.6*(10^ -19) C

B = 8.46*(10^ -3)

r = 0.1356 m

Diameter = 0.271 m = 27.1 cm

(c)Sepration = D1 - D2 = 27.1 -25 = 2.1 cm

On the scale of atoms it is large enough to be observed

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