Mass Spectrometer and Charge-to-Mass Separation
After a velocity selector v = E/B_s, an analyzing field B_a gives r = mv/(|q|B_a). If ions are accelerated through V instead, r^2 = 2mV/(|q|B_a^2).
Why this shows up in the exam
Isotope separation · Identifying ion charge states · Detector-position and mass-ratio questions
Learn the idea
Known-speed ions separate in a magnetic field because orbit radius measures momentum per charge. A selector first makes velocities equal; then heavier ions bend less and land at different detector positions. The apparatus turns track geometry into mass-to-charge information.
🧠 Memory hook: Select the speed, bend the beam, read mass-to-charge from radius.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- v = E/B_s — speed selected by crossed fields
- m/|q| = r B_a/v — mass-to-charge ratio from known speed and orbit radius
- m/|q| = r² B_a²/(2V) — mass-to-charge ratio after acceleration through V
How to approach it
- 1Identify how speed is set
- 2Apply r = mv/(|q|B) in the analyzer
- 3Relate measured geometry to radius and compare m/|q|
Common slip-ups that cost marks
- •Using the selector and analyzer fields interchangeably
- •Comparing masses without checking charge states
- •Using diameter as radius
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A charge of 2 microC moves perpendicular to a 3 T magnetic field at 4 x 10^5 m/s. Find the magnetic force.
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