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Determining Diet. One method for determining the amount of corn 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 12Cand 13Cisotopes in samples of human remains. Suppose you use a velocity selector to obtain singly ionized (missing one electron) atoms of speed , and you want to bend them within a uniform magnetic field in a semicircle of diameter cm for the . The measured masses of these isotopes are 1.99ร—10โˆ’26kg(12C)and2.16ร—10โˆ’26kg(13C)and (a) What strength of magnetic field is required? (b) What is the diameter of the13Csemicircle? (c) What is the separation of the and ions at the detector at the end of the semicircle? Is this distance large enough to be easily observed?

Short Answer

Expert verified

(a) The strength of magnetic field is required isB=8.46ร—10-3T

(b) The diameter of the 13C semicircle isR13=13.6cm

(c) The separation of the 12C and 13C ions at the detector at the end of the semicircle is2R13-R12=2.2cm .

Step by step solution

01

Definition of Magnetic field

The term magnetic field may be defined as the area around the magnet behave like a magnet.

02

Determine the strength of magnetic field is required and the diameter of the 13C semicircle.

The strength of magnetic field can be calculated asB=mv|q|R12

Put the all values

B=1.99ร—10โˆ’26kg8.50ร—103m/s1.60ร—10โˆ’19C(0.125m)B=8.46ร—10โˆ’3T

Hence, the strength of magnetic field is required isB=8.46ร—10โˆ’3T.

According to the result R=mv|q|BExcept radius of curvature and mass rest all variables area constant for the 13C,12C.

So

Rm=v|q|BR12m12=R13m13R13=R12m13m12PutallthevaluesR13=(12.5cm)2.16ร—10โˆ’26kg1.66ร—10โˆ’26kgR13=13.6cm

Hence, the diameter of the 13C semicircle isR13=13.6cm.

And the separation of 12C,13Ccan be calculated as

2R13โˆ’R12=2(13.6cmโˆ’12.5cm)2R13โˆ’R12=2.2cm

Hence, the separation of the 12C and 13C ions at the detector at the end of the semicircle is2R13โˆ’R12=2.2cm .

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