Chapter 20, Problem 24P

Ancient meat eating. 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 ¹⁵N, 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) nitrogen atoms of speed 8.50 km/s and bend them along a semicircle within a uniform magnetic field If the ¹⁴N atoms travel along a semicircle with a diameter of 29.2 cm, find the separation of the ¹⁴N and ¹⁵N isotopes at the detector. The measured masses of these isotopes are 2.32 × 10⁻²⁶ kg (¹⁴N) and 2.49 × 10⁻²⁶ kg (¹⁵N).