Consider the mass spectrometer shown schematically in Figure...

Consider the mass spectrometer shown schematically in Figure 29.24 . The magnitude of the electric field between the plates of the velocity selector is $2500 \mathrm{V} / \mathrm{m},$ and the magnetic field in both the velocity selector and the deflection chamber has a magnitude of 0.0350 $\mathrm{T}$ Calculate the radius of the path for a singly charged ion having a mass $m=2.18 \times 10^{-26} \mathrm{kg}$ .

Key Concepts

Mass Spectrometry

Mass spectrometry is an analytical method used to determine the composition and structure of substances by ionizing sample molecules and analyzing the resulting charged particles. It separates ions based on their mass-to-charge ratios, enabling precise measurements and identification of the constituent elements or compounds.

Velocity Selector

A velocity selector is a component in instruments such as mass spectrometers that uses perpendicular electric and magnetic fields to filter particles according to their speeds. Only ions with a specific velocity pass through the selector undeflected, ensuring a uniform velocity for subsequent analysis.

Lorentz Force

The Lorentz force is the force exerted on a charged particle moving in electric and magnetic fields, expressed as F = q(E + v × B). This force is fundamental in changing the motion of the charged particles, causing deflection and enabling control over their trajectories in instruments like mass spectrometers.

Circular Motion of Charged Particles in a Magnetic Field

When a charged particle enters a uniform magnetic field perpendicular to its velocity, it experiences a force that acts perpendicular to its motion, causing it to travel in a circular path. The radius of the circular path is determined by the balance of the magnetic Lorentz force and the centripetal force required for circular motion, as described by the relation r = mv/(qB).

Charge-to-Mass Ratio

The charge-to-mass ratio (q/m) is a critical parameter in mass spectrometry that influences how ions move in electromagnetic fields. By measuring the curvature of the ion paths in magnetic fields, one can accurately deduce this ratio, which is essential for identifying the types of ions present in a sample.

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