The mass spectrometer

The particles leaving the selector with velocity $v = E/B_1$ then enter a second region with only a magnetic field $B_2$. Here, since $\vec{v}\perp\vec{B}_2$, they curve along circles of radius

$r = \frac{m\,v}{q\,B_2} = \frac{m}{q}\cdot\frac{E}{B_1 B_2}$

With $E$, $B_1$, $B_2$ fixed by the instrument, the radius depends only on the ratio $m/q$. Measuring $r$ (for example with a photographic plate) gives the mass per unit charge.

Principle — Bainbridge spectrometer

Combining a velocity selector $v = E/B_1$ with a magnetic-field chamber $B_2$, the radius of the circular trajectory is proportional to $m/q$: ions with the same charge separate by mass.

Example — Uranium isotopes

To separate ${}^{235}\text{U}$ from ${}^{238}\text{U}$, ionised to $q = +e$ and selected at $v \approx 10^6\;\text{m/s}$ in a field $B_2 = 0{,}5\;\text{T}$, the radii are $r = mv/(eB_2) \approx 4{,}9\;\text{cm}$ and $4{,}96\;\text{cm}$. A spatial separation of $\sim 0{,}6\;\text{mm}$ sounds microscopic, but on an industrial scale (chambers metres long) it is enough to separate the two species. This is the electromagnetic “calutron” method used at Oak Ridge during the Manhattan Project (Rhodes 1986).

The mass spectrometer is today one of the most widely used analytical instruments: it identifies molecules from their mass in chemistry, biology, anti-doping controls and isotopic dating.

Links

Topics: Magnetismo Concepts: Forza di Lorentz · Moto circolare uniforme

Related exercises: Frequenza di ciclotrone di un protone · Esercizio svolto — deflettore di ioni · Raggio e periodo di un elettrone