Bainbridge's mass spectrometer, shown in Fig. 28-54 ,...

Bainbridge's mass spectrometer, shown in Fig. $28-54$ , separates ions having the same velocity. The ions, after entering through slits, $S_{1}$ and $S_{2}$ pass through a velocity selector composed of an electric field produced by the charged plates $P$ and $P^{\prime},$ and a magnetic field $\vec{B}$ perpendicular to the electric ficld and the ion path. The ions that then pass undeviated through the crossed $\vec{E}$ and $\vec{B}$ fields enter into a region where a second magnetic field $\vec{B}$ ' exists, where they are made to follow circular paths. A photographic plate (or a modern detector) registers their arrival. Show that, for the ions, $q / m=E / r B B^{\prime},$ where $r$ is the radius of the circular orbit.

Bainbridge's mass spectrometer, shown in Fig. $28-54$ , separates ions
having the same velocity. The ions, after entering through slits, $S_{1}$ and $S_{2}$ pass through a velocity selector composed of an electric field produced by the charged plates $P$ and $P^{\prime},$ and a magnetic field $\vec{B}$ perpendicular to the electric ficld and the ion path. The
ions that then pass undeviated through the crossed $\vec{E}$ and $\vec{B}$ fields enter into a region where a second magnetic field $\vec{B}$ ' exists, where they are made to follow circular
paths. A photographic plate (or a modern detector) registers their
arrival. Show that, for the ions, $q / m=E / r B B^{\prime},$ where $r$ is the radius
of the circular orbit.

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Key Concepts

Mass Spectrometry

Mass spectrometry is an analytical technique that separates ions based on their mass-to-charge ratio by using electric and magnetic fields to influence their trajectories. This separation enables the identification and quantification of different components in a sample.

Velocity Selector

A velocity selector uses crossed electric and magnetic fields oriented perpendicular to each other to filter ions by velocity. Only particles that travel at a specific speed, typically determined by the ratio between the electric field strength and the magnetic field strength, will pass through undeviated.

Circular Motion in a Magnetic Field

When ions enter a region with a uniform magnetic field, they experience a constant magnetic force that acts as the centripetal force, causing them to move in circular paths. The balance between this magnetic force (qvB) and the required centripetal force (mv²/r) leads to relations that connect the ion's mass, charge, velocity, and the magnetic field strength.

Lorentz Force

The Lorentz force is the force exerted on a charged particle moving through electric and magnetic fields, calculated as the sum of the electric force (qE) and the magnetic force (qvB). It is fundamental in understanding how charged particles are deflected or guided in devices like mass spectrometers.

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