The amount of meat in prehistoric diets can be determined by measuring the ratio

Question

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 9.05 km/s and bend them along a semicircle within a uniform magnetic field. The 14N atoms travel along a semicircle with a diameter of 20.0 cm . The measured masses of these isotopes are 2.32×1026 kg (14N ) and 2.49×1026 kg for (15N ).

Part A

Find the separation of the 14N and 15N isotopes at the detector.

Express your answer in centimeters.

Explanation / Answer

formula for radius of velocity selector

Formula

r = mv/ qB

for (C-12)

r C=m(C-12)v/qB

for (N-14)

r N=m(N-14)v/qB

for (N-15)

r N-15=m(N-15)v/qB

take ratio of C-12 to N-14

r N-14 =rC*m(N-14)/m(C-12)

=20cm*2.32×10-26/1.99×10-26

=23.31cm

take ratio of N-15 toC-12

r N-15 =rC*m(N-15)/m(C-12)

=20cm*2.49×10-26/1.99×10-26

=25.02cm

the separation of the 14N and 15N isotopes at the detector is

25.02cm - 23.31cm = 1.71cm

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

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