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 N-15, 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) atoms of speed 8.50 km/s and want to bend them within a uniform magnetic field in a semicircle of diameter 25.0 cm for the C-12. The measured masses of these isotopes are 2.32×10-26 kg (N-14), 1.99×10-26 kg (C-12) and 2.49×10-26 kg (N-15).
Find the separation of the N-14 and N-15 isotopes at the detector.

Explanation / Answer

The radius R is determined by the formula

R = mv/qB,

q=same for all, +1, because they all lack 1 electron.

B = magnetic field is the same for all,

v = 8.5 km/s is described to be the same for all

Thus,

R(C-12)=m(C-12)v/qB --------(1)

R(N-14)=m(N-14)v/qB--------(2)

R(N-15)=m(N-15)v/qB---------(3)

Dividing (1) by (2),we have

R(C-12)/R(N-14)=m(C-12)/m(N-14)

R(N-14)=R(C-12)*m(N-14)/m(C-12)

=25*2.32×10-26/1.99×10-26

=29.14673 cm

Dividing (1) by (3),we have

R(C-12)/R(N-15)=m(C-12)/m(N-15)

R(N-15)=R(C-12)*m(N-15)/m(C-12)

=25*2.49×10-26/1.99×10-26

=31.28141 cm

The separation of the N-14 and N-15 isotopes at the detector :

Separation=31.28141-29.14673 =2.135 cm or 2.14 cm

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

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