Cyclotron
Mass spectrometer — sort isotopes. Builds on Lorentz Force.
In a mass spectrometer, two ions with the same charge (+e) but different masses enter a uniform magnetic field. Ion A has mass m, and Ion B has mass 2m. Both enter the field at the same speed v.
Compared to Ion A, what happens to Ion B’s circular path?
Ion B curves into a circle with TWICE the radius! From r = mv/(qB), doubling the mass doubles the radius. The heavier ion’s greater inertia resists the magnetic steering force, so it swings wider. This is the principle behind every mass spectrometer — different masses land at different positions on the detector.
Loading simulation…
Watch two isotopes (different colors) enter the same B-field at the same speed. The heavier one curves into a larger semicircle and hits the detector farther from the entrance. This is how scientists identify atoms.
r = mv / (qB)
Same charge, same speed, same field — the only difference is mass. Heavier particles make bigger circles. This one equation is the heart of mass spectrometry.
Used in chemistry, biology, and forensics to identify unknown substances. A sample is ionized and sorted by mass in a magnetic field — the mass spectrum is like a fingerprint for molecules.
During the Manhattan Project, electromagnetic separation (calutrons) used this principle to separate uranium-235 from uranium-238. The lighter isotope curves slightly tighter, allowing collection.
Accelerator mass spectrometry counts individual carbon-14 atoms by separating them from carbon-12 in a magnetic field. This allows dating of archaeological samples thousands of years old.
Hospital cyclotrons accelerate protons using spiraling paths in a magnetic field, then smash them into targets to produce radioactive isotopes for PET scans and cancer therapy.
“One equation — r = mv/(qB) — lets us weigh atoms, date ancient relics, enrich uranium, and treat cancer. The magnetic force doesn’t just steer particles; it reveals their identity.”
Cyclotron Lab
Build your own cyclotron! Watch a charged particle spiral outward as it gains energy with each pass through the accelerating gap. Adjust the magnetic field, AC frequency, and particle mass to see how the spiral changes. Can you get the timing just right for resonance?
Loading simulation…
Start with the default settings and watch the particle spiral outward. Notice how each semicircle is bigger than the last — the particle is gaining speed. Now try increasing the B-field: the spirals get tighter. Mismatch the AC frequency and watch the particle lose sync with the accelerating voltage. Try a heavier particle — it spirals out faster because each semicircle has a larger radius.
In a cyclotron, the orbital period T = 2πm/(qB) is independent of speed! A faster particle makes a bigger circle but traverses it in the same time. This means a fixed-frequency AC voltage stays in sync with the particle — the key insight that makes cyclotrons work.