D.3 · IB Physics
Mass spectrometer
Accelerate ions through a potential difference, send them into a uniform magnetic field and watch isotopes of different mass land at different points on the detector.
The drawing rescales automatically when paths get very large or small: read distances from the ruler along the detector.
qV = ½mv² ⇒ v = √(2qV/m)
qvB = mv²/r ⇒ r = mv/(qB)
so r = (1/B)√(2mV/q)
impact point: x = 2r from slit
1 u = 1.66 × 10⁻²⁷ kg, e = 1.60 × 10⁻¹⁹ C
Try this
- With neon at 1000 V and 0.50 T, note the separation Δx. Double V to 2000 V: does Δx double? Explain using r ∝ √V.
- Choose Custom with m = 20 u and charge +2e. Which mass of singly charged ion would land in exactly the same place? Check it.
- For chlorine at 2000 V, find the field B that makes the ³⁵Cl⁺ and ³⁷Cl⁺ impact points 1.00 cm apart.
Exam tip: combine ½mv² = qV with r = mv/(qB) to get r = √(2mV/q)/B, and remember the detector separation is the difference in diameters, 2(r₂ − r₁), not the difference in radii.