CHEM 5181 – Fall 2006 Homework Assignment #3 Assigned 21-Sept / Due 3-Oct Problem 1. Calculate the mass analyzer resolving power (using FWHM for m, as we defined it in class) needed to separate CO+ and N2+, and also to separate C3H7+ and C2H3O+. Assume that (a) the peaks have Gaussian shapes; (b) both peaks have the same total intensity; (c) the separation is acceptable for our analysis purposes when the valley between two peaks in the spectrum is less than 10% of the peak value. Problem 2. The figure below represents the simplified stability diagram of a quadrupole for three ions of masses m1, m2, and m3 (singly charged) vs. U and V. Explain which ions will / will not be observed as the values of U and V are changed from point A to point G in the figure. A E D F B D B G A E G C Problem 3. In a 1997 paper (J. Am. Soc. Mass Spec. 8(3), 209, 1997) Martin Vestal and co-workers used a linear TOFMS with a delayed extraction source (modified PerSeptive Biosystems Voyager RP) to measure the initial velocity distribution of ions generated by MALDI. In this problem, you will predict the distribution of recorded flight times for the singly charged insulin ion (MW = 5733.50) based on initial velocity distributions and TOFMS parameters reported in that paper. The basic schematic is identical to the sketch of the linear TOFMS that you drew in lab #1. The distance (d1) between the back plate (V0) and the first grid (V1) is 0.39 cm The distance (d2) between the first grid and the grid at the beginning of the drift region (V2) is 1.48 cm The total length of the drift region (D) between V2 and the detector is 128.9 cm The voltage applied V0 is 20 kV The voltage applied to V1 for extraction is 90% of the voltage applied to V0, or 18 kV. V2 and the detector are held at ground. The insulin ions have a mean initial velocity along the TOF axis of 300 m / sec, and range from 0 to 600 m/sec. An Excel spreadsheet has been provided (on the course web page) as a guide for solving this problem. You are not required to use it, but the printed results you submit should include tables similar to those in the spreadsheet and a plot of the flight times of 7 ions (of different initial velocity) as a function of delay time. Cells of the Excel spreadsheet are colored in order to indicate what is provided as an input, and what requires calculation by you. These steps will guide you through the spreadsheet: a. Within the spreadsheet, fill in the cells corresponding to the field strengths in the regions between V0 and V1 (E1) and V1 and V2 (E2), the charge of the ion in Coulombs, and the mass of a single ion in kg. These will be critical values for the calculations that follow. b. s’ denotes the distance between an ion and V1 at the moment of acceleration. Ions originate at V0; prior to the extraction event (i.e., during the delay), ions drift away from the V0 at an initial velocity originating from the ionization event. [i] Write an expression for s’ as a function of initial velocity (vo) and delay time (td) and use this expression to calculate values for column C in the spreadsheet. c. As it passes through the first grid, an ion will have a kinetic energy (U1) that is the sum of its initial energy (Uo) and the energy derived from acceleration (Ua1). Write expressions for [i]U1 in terms of Uo and Ua1 [i] Uo in terms initial velocity (vo) and [ii] Ua1 in terms of the electric field in this first region (E1), s’, q, and m. [iii] the velocity of the ion as it passes through the first grid (v1) in terms of U1. Use these expressions to calculate values for column D. d. Force can be written as the product of mass (m) and acceleration (a) or as the product of electric field (E) and charge (q). [i] Based on this, write a general expression for a in terms of E, q, and m. Denote the units of each variable. Use this expression to solve for the acceleration that occurs in region 1 (a1) and use that expression to find values for Column E. e. A body undergoing constant acceleration, a, for a time, t, will reach a final velocity, vf, that is equal to the initial velocity, vo, plus the product, ta. [i] Use this fact to write an expression for the time spent in region 1 (T1) after the acceleration event in terms of vo , v1 and a1. Use this expression to solve for values in Column F. f. Next, we must determine the amount of time an ion will spend traveling through the region between V1 and V2 (Region 2). As in Region 1, the energy that an ion has (U2) as it crosses V2 will be a sum of the energy it had upon entering Region 2 (U1) and the energy it gained by acceleration in Region 2 (Ua2). [i] Write an expression for the velocity of an ion at V2 as a function of Uo, U1, and Ua2. [ii] Write an expression for Ua2 in terms of the electric field in region 2 (E2). Use these expressions (and previous expressions for Uo and U1) to solve for the ion velocities at the exit of Region 2 (v2). (Column G) g. Use methods similar to parts c and d to complete columns H and I of the spreadsheet. h. Upon exiting Region 2, an ion enters the field-free drift region of the TOFMS. It will undergo no more acceleration. Its velocity thus remains constant. [i] Write an expression for the time an ion spends in the drift region in terms of the length of the drift region (D) and its velocity upon exiting Region 2 (v2). Use this expression to solve for the time spent in the drift region (TD). i. An ions total flight time (TTotal) is the sum of time spent in Region 1, Region 2, and the Drift Region. Use this fact to complete Column K. (For comparison, Vestal reports times around 51 microsec. Your value should be close to this.) j. You now have a working model of the PerSeptive Biosystems Voyager RP TOFMS. As a final step in the problem, we must determine the best delay time, which is the delay time that minimizes the distribution in ion times of flight. Vary delay time in your spreadsheet and generate a plot of flight times as a function of delay time. This can be done by copying calculated values from cells K35-K41 to the corresponding cells in rows 45-51. k. Print your results, including all cells of the spreadsheet and the generated plot. Which delay time is optimum?