The strengths of the fields in the velocity selector of a...

The strengths of the fields in the velocity selector of a Bainbridge mass spectrometer are $B=0.500 \mathrm{T}$ and $E=$ $1.2 \times 10^{5} \mathrm{V} / \mathrm{m}, \quad$ and the strength of the magnetic field that separates the ions is $B_{o}=0.750 \mathrm{T}$. A stream of singly charged Li ions is found to bend in a circular arc of radius 2.32 $\mathrm{cm} .$ What is the mass of the Li ions?

Key Concepts

Mass Spectrometry

Mass spectrometry is an analytical technique used to determine the mass-to-charge ratio of ions. It typically involves ionizing the sample, selecting ions of a specific velocity or energy, and then using electric and magnetic fields to separate these ions based on their masses, making it possible to identify and quantify the components of a mixture.

Velocity Selector

A velocity selector is a device used to ensure that only particles with a specific speed pass through undeflected. It uses perpendicular electric and magnetic fields such that the electric force and magnetic force on a charged particle cancel each other for particles moving at a particular velocity, allowing for the selection of ions with that precise speed.

Lorentz Force

The Lorentz force is the force experienced by a charged particle moving within electromagnetic fields, given by the equation F = q(E + v × B). In mass spectrometry, this force is fundamental in manipulating the trajectory of ions, either by using the electric component to select a specific velocity or by using the magnetic component to bend their path for mass analysis.

Circular Motion in Magnetic Fields

When a charged particle with velocity perpendicular to a magnetic field enters that field, it experiences a magnetic force that acts as a centripetal force. This force causes the particle to move in a circular path, where the balance between the magnetic force (qvB) and the required centripetal force (mv²/r) enables calculations of particle properties such as mass when their trajectory radius is known.

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