Mathematical routines (MR)
Separating neon isotopes in a mass spectrometer
- Units 10 and 12
- 10 points
- About 22 minutes
You can use a calculator on this question, just like on exam day.
A multipart problem where you use math to analyze a physical situation. You draw or sketch a representation such as a circuit diagram, a ray diagram or a graph, derive an equation using letters, calculate a numerical answer with units, and then make a claim or prediction and justify it with physics reasoning. On the exam: Question 1 of 4. New for May 2027: the free-response section is 95 minutes, down from 100, for all 4 questions (50% of your score), one of each type in this order. Calculator and equation sheet allowed. The CED suggests 20–25 minutes. This question type started in May 2025, so Physics 2 free-response questions from 2024 and earlier are built differently.
The question
In a mass spectrometer, singly charged positive neon ions (charge +e) start from rest and are accelerated through a potential difference of 2000 V. They then pass through a slit into a region of uniform magnetic field of magnitude 0.25 T, which is perpendicular to the plane of the page. The ions enter the field moving to the right, in the plane of the page, curve toward the top of the page, travel in a semicircle, and strike a detector plate in line with the slit. Neon has two common isotopes: neon-20 (mass 20 u) and neon-22 (mass 22 u). Use 1 u = 1.66 × 10⁻²⁷ kg and e = 1.60 × 10⁻¹⁹ C, and ignore gravity.
Suggested time: 22 minutes
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Part (a)
2 points(i) State the direction of the magnetic field and justify your answer. (ii) Describe the force diagram for an ion in the field, and explain why its speed does not change.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
Part (b)
3 pointsDerive an expression for the distance D from the slit to the point where an ion strikes the detector, in terms of the ion's mass m, the charge e, the accelerating potential difference ΔV, and the magnetic field B.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
Part (c)
2 pointsCalculate (i) the speed of a neon-20 ion as it enters the field and (ii) the distance D for a neon-20 ion.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
Part (d)
2 pointsDo neon-22 ions strike the detector closer to the slit than neon-20 ions, farther from it, or at the same place? Justify your claim using your expression from part (b).
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
Part (e)
1 pointCalculate the distance between the points where the neon-20 and neon-22 ions strike the detector.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
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