One method for determining the amount of com in early Native American diets is t

Question

One method for determining the amount of com in early Native American diets is the stable isotope ratio analysis (SIRA) technique. As corn photosynthesizes, it concentrates the isotope carbon-13, whereas most other plants concentrate carbon-12. Overreliance on corn consumption can then be correlated with certain diseases, because corn lacks the essential amino acid lysine. Archaeologists use a mass spectrometer to separate the ^12 C and ^13 C isotopes in samples of human remains. Suppose you use a velocity selector to obtain singly ionized (missing one electron) atoms of speed 8.50km/s, and you want to bend them within a uniform magnetic field in a semicircle of diameter 25.0 cm for the ^12 C. The measured masses of these isotopes are 1.99 times 10^-26 kg (^12 C) and 2.16 times 10-26 kg (^13 C). What strength of magnetic field is required? What is the diameter of the ^13 C semicircle? What is the separation of the ^12 C and ^13 C ions at the detector at the end of the semicircle? Is the distance found in part C large enough to be easily observed?

Explanation / Answer

in veloity selector,

let mass of the ion be m, speed v, magnetic field B and radius r.

as it is signly ionized, charge=q=1.6*10^(-19) C

then balaning centripetal force by magneti force:

m*v^2/r=q*v*B

==>B=m*v/(q*r)

part a:

using given values:

m=mass of C12=1.99*10^(-26) kg
v=speed=8.5 km/s=8.5*1000 m/s
radius=diameter/2=25 cm/2=0.25/2 m
then

B=1.99*10^(-26)*8.5*1000/(1.6*10^(-19)*0.25/2)

=0.0084575 T

part B:

for 13C, m=2.16*10^(-26) kg

then r=m*v/(q*B)

=2.16*10^(-26)*8.5*1000/(1.6*10^(-19)*0.0084575)

=0.13568 m

daimeter=radius*2=0.27136 m=27.136 cm

part C:

separation=difference between diamters
=27.136-25=2.136 cm

part D:

2.136 cm is large enough to be observable.

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