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.?

Complete Question

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The relative separation of  ¹⁴N and ¹⁵N at the detector is 2.0 cm

Explanation:

In order to gain a better understand of some concepts

Mass Spectrometer:

This is an instrument or an apparatus that can be use to measure masses of isotopes,molecular fragments and molecules,enabling precise measurement of the isotopic composition.The way it does this is by ionizing them and determining their paths in an electric and a magnetic fields.

This device is consist of three parts which include:

i) ion source

ii) mass analyser

iii) ion detector

This device sort out ions by mass,because  ¹⁴N and ¹⁵N have different masses it is possible use this device to separate them

Process and Calculation:

When the mass spectrometer has been set to ultra high vacuum condition(10⁻⁶ to 10⁻⁹) by pumping it. The ¹⁴N and  ¹⁵N isotopes ion is inputted into the ion source as a gas,here it would be bombarded with electrons.The resulting ions(with charge q) will then be hurried up in an electric field (having a potential difference of V) and then be assimilated into a narrow beam. this beam is sent through a magnetic field (having strength H) which deflects it into a circular trajectory with a radius(R) proportional to the mass (M).This results to a physical separation of the incoming ion beam into various outgoing beams.The desired beam is steered into the ion detector .

   The mass analyser deflects the ions using the following formula:

re-arranging this formula and eliminating one v

we are given that mass of carbon = 1.99 × 10⁻²⁶

and the radius of carbon = 12.5 cm.

   The separation of the isotopes at the detector

is 2(R₁₅ -  R₁₄).

extracting the constants;

      :

real, smaller and upside-down.   so the answer should be b.