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Measuring the approximate mass of an ion without using a standard can he accomplished via the following variant of the peak-matching technique described in Problem 20-14. The peak-matching technique is used to alternately cause the pion and the (P + I) ^{+} ions to reach the detector. It is assumed that the difference in mass between p+ and (P + I)^{ -} is due to a single ^{13}C replacing a ^{12}C atom.
(a) If the accelerating voltage for (P + 1)^{+} is labeled V_{2}, and that for P^{-} is V_{1} derive a relationship that relates the ratio V_{2}/V_{1}, to the mass of P^{+}.
(b) If V_{2}/V_{1} = 0.987753, calculate the mass of the P^{+} ion.
Problem 20-14
In a magnetic sector (single-focusing) mass spectrometer, it might be reasonable under some circumstances to monitor one m/z value, to then monitor a second m/z. and to repeat this pattern in a cyclic manner. Rapidly switching between two accelerating voltages while keeping all other conditions constant is called peak matching
(a) Derive a general expression that relates the ratio of the accelerating voltages to the ratio of the corresponding m/z values.
(b) Use this equation to calculate m/z of an unknown peak if m/z of the ion used as a standard, CF_{3}^{+}, is 69.00 and the ratio of V _{unknown} /V _{standard} is 0.965035.
(c) Based on your answer in part (b), and the assumption that the unknown is an organic compound that has a mass of 143, draw some conclusions about your answer in part (b), and about the compound.
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