Determining Diet. 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 * 10-26 kg (12C) and 2.16 * 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 be easily observed?

Determining Diet. 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 * 10^-26 kg (¹²C) and 2.16 * 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 be easily observed?