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Sears and Zemansky's University Physics with Modern Physics | 13th Edition | ISBN: 9780321696861 | Authors: Hugh D. Young; Roger A. Freedman; A. Lewis Ford
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BIO Determining Diet. One method for determining the

Chapter 27, Problem 73P

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Problem 73P

BIO 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 12C and 13C isotopes in samples of human remains. Suppose you use a velocity selector to obtain singly ionized (missing one electron) atoms of speed 8.50 km/s, and you want to bend them within a uniform magnetic field in a semicircle of diameter 25.0 cm for the 12C. The measured masses of these isotopes are 1.99 × 10-26 kg (12C) and 2.16 × 10-26 kg (13C). (a) What strength of magnetic field is required? (b) What is the diameter of the 13C semicircle? (c) What is the separation of the 12C and 13C ions at the detector at the end of the semicircle? Is this distance large enough to be easily observed?

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QUESTION:

Problem 73P

BIO 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 12C and 13C isotopes in samples of human remains. Suppose you use a velocity selector to obtain singly ionized (missing one electron) atoms of speed 8.50 km/s, and you want to bend them within a uniform magnetic field in a semicircle of diameter 25.0 cm for the 12C. The measured masses of these isotopes are 1.99 × 10-26 kg (12C) and 2.16 × 10-26 kg (13C). (a) What strength of magnetic field is required? (b) What is the diameter of the 13C semicircle? (c) What is the separation of the 12C and 13C ions at the detector at the end of the semicircle? Is this distance large enough to be easily observed?

ANSWER:

Solution 73P

Introduction

At first we have to calculate the strength of the magnetic field to bend the 12C at a semicircular path of diameter of 25.0 cm.

Then we have to calculate the diameter of the path of 13C.

Then we have to calculate the separation between the 12C and 13C in the detector and we have discuss if the separation is sufficient to observe.

Step 1

The radius of charge particle in the uniform magnetic field is given by

Here  is the mass  is the magnitude velocity and  is the charge of the particle. B is the strength of magnetic field.

So we have

Now we know that, for 12C,

And

Now since the isotopes are singly ionized, the charge of the isotope will be equal to the charge of electron and since the ion is a positive ion the sign of the charge is positive. Hence we have

Hence strength of the magnetic field is

So the strength of the magnetic field is  T.

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