Conceptual Physics

Physics principles and equations

The relationship between angular velocity and tangential speed is

v = rȦ

The radius of a particle’s circular motion in a magnetic field is

Step-by-step solution

Step Reason

1. v = rȦ angular velocity and speed

2. radius of circular motion in a magnetic field

3. substitute equation 1 into equation 2

4. simplify and solve for B

5. evaluate

28.15 - Physics at work: mass spectrometer

Mass spectrometers are used to determine the masses of atoms or molecules, or their

relative abundance in a sample. They are used in a range of settings from surgery (to

determine the mixture of gases in a patient’s lungs) to space missions (to analyze the

atmospheres or soils of planets and other celestial bodies). Chemists also frequently

use them to analyze materials.

A conceptual diagram of a mass spectrometer is shown to the right. To use the device,

the substance being analyzed is first vaporized if it is not already a gas. It is then

ionized: An electron is removed from each particle so that it has a net positive charge

equal to +e. The ionized particles are then accelerated across a potential difference

between two charged plates.

The particles all have the same charge, and the experimenter keeps the potential

difference between the plates, and the resulting electric field strength, at a constant

value. This means the force exerted on various particles by the electric field does not

change; their accelerations depend only on their masses.

Each moving, charged particle passes through an entry port into a uniform magnetic

field. The field is perpendicular to the velocity of the particle, which means the particle

will move in a circular path. The magnetic field is kept constant so that the radius of the

path is a function of the particle’s speed and mass.

Each particle traverses a circular path and the point where it strikes the sensing plate of

the device is recorded. The radius of the path is one-half the distance from the entry

port. The particle’s mass can be determined using the equation shown to the right.

Determining the mass of a particle (Derivation). In the following derivation we

assume that the ion has a charge of +e, so that it is accelerated from the positively

charged plate to the negatively charged plate, and then curves to the right after it enters

the magnetic field, which is directed out of the screen toward you.

Mass spectrometer

Device that measures mass of particles

Electric field accelerates ions

Radius measured to determine mass

Mass of a particle

(^518) Copyright 2000-2007 Kinetic Books Co. Chapter 28