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 a 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 8.50 km/s, and you 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 distance large enough to he easily observed?

Explanation / Answer

a.) Centripital force is provided by the force due to magnetic field

For 12C

mass of carbon atom = 1.99 * 10 ^ -26 Kg

Charge on carbon atom = + e = 1.6 * 10 ^ -19 C

Velocity of carbon atom = 8.5 km/s = 8500 m/s

radius of semicirlce = 25 / 2 = 12.5 cm

therefore

q * v * B = m * v^2 / r

B = m * v / ( q * r )

= ( 1.99 * 10 ^ -26 * 8500 ) / ( 1.6 * 10 ^ -19 * 0.125 )

= 8.44 * 10 ^ -3 T ans

b.) Mass of 13C = 2.16 * 10 ^ -26 Kg )

B = ( 2.16 * 10 ^ -26 * 8500 ) / ( 1.6 * 10 ^ -19 * r )

r = ( 2.16 * 10 ^ -26 * 8500 ) / ( 1.6 * 10 ^ -19 * 8.44 * 10 ^ -3 )

= 0.1358 m

therefore, diameter of the 13C semicircle = 2 * 13.58 = 27.15 cm ans

c.) Sepration of 12 C and 13C = 13.58 - 12.5 = 1.08 cm

Yes, the distance is large enough to be easily observed

Related Questions

Navigate

• Browse (All)
• Browse O
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.