Translation between representations (TBR)
Sorting ions in a mass spectrometer
- Units 9 and 12
- 12 points
- About 28 minutes
You can use a calculator on this question, just like on exam day.
A multipart problem about one situation shown in several ways. You draw a diagram, derive equations, sketch or draw graphs, and then explain whether your answers agree with each other or use them to predict what happens when the situation changes. On the exam: Question 2 of 4. Section II has 4 questions in 95 minutes (50% of the exam score), one of each type in this order; calculator and equation sheet allowed. The CED suggests 25–30 minutes.
The question
In a mass spectrometer, positive ions of charge +q and mass m start from rest and are accelerated through a potential difference ΔV. Each ion then passes through a small opening at point P in a straight, horizontal wall and enters a region of uniform magnetic field of magnitude B, directed into the page. As it enters, the ion is moving straight up the page, perpendicular to the wall. The field fills the whole region above the wall. The ion travels in the plane of the page until it strikes a detector lying along the wall. Gravity is negligible.
Suggested time: 28 minutes
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Part (a)
2 pointsDescribe the force diagram for an ion just after it enters the magnetic field at P: list every force and give its direction. Then explain why the ion's speed stays constant while it is in the field.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
Part (b)
2 pointsDerive an expression for the speed v of an ion as it enters the magnetic field, in terms of q, m, and ΔV.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
Part (c)
2 pointsDerive an expression for the distance d from P to the point where the ion strikes the detector, in terms of q, m, ΔV, and B.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
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Part (d)
3 pointsStudents vary ΔV for one kind of ion and measure d each time. (i) Describe the graph of d as a function of ΔV. (ii) Which quantities should they graph to get a straight line, and what would the slope of that line equal?
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
Part (e)
3 pointsTwo isotopes of the same element have the same charge q. One has mass m, and the other has mass 1.10m. Both are accelerated through the same ΔV and enter the same field. (i) Which isotope strikes the detector farther from P? (ii) Calculate the ratio of their distances. (iii) Explain how your answer is consistent with the graph you described in part (d)(ii).
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
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