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Chapter 4: Q33E (page 914)

The amount of meat in prehistoric diets can be determined by measuring the ratio of the isotopes 15N to 14N in bone from human remains. Carnivores concentrate 15N, so this ratio tells archaeologists how much meat was consumed. For a mass spectrometer that has a path radius of 12.5 cm for 12C ions (mass 1.99 * 10-26 kg), find the separation of the 14N (mass 2.32 * 10-26 kg) and 15N (mass 2.49 * 10-26 kg) isotopes at the detector.

Short Answer

Expert verified

The separation of the 14N and 15N isotopes at the detector is 2.1357cm

Step by step solution

01

Path radius

Path radius in a magnetic field of a particle is given by

R=mvqB

02

Determine the separation

Path radius is given by

R=mvqB

Therefore, path radius of 14N is

RN14=(2.32脳10鈭�261.99脳10鈭�26)(252)=14.5729cm

The path of the isotope

DN14=(14.5729)(2)=29.1457cm

Now the radius of the 15Nis

RN15=(2.49脳10鈭�261.99脳10鈭�26)(252)=15.6407cm

Therefore, the path is

DN15=(15.6407)(2)=31.2814cm

Therefore, the separation will be

DN15鈭�DN14=31.2814鈭�29.1457=2.1357cm

Therefore, the separation of the 14N and 15N isotopes at the detector is 2.1357cm

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