Chapter 19, Problem 21P

### College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

Chapter
Section

### College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

# A particle passes through a mass spectrometer as illustrated in Figure P19.15. The electric field between the plates of the velocity selector has a magnitude of 8 250 V/m, and the magnetic fields in both the velocity selector and the deflection chamber have magnitudes of 0.093 1 T. In the deflection chamber the particle strikes a photographic plate 39.6 cm removed from its exit point alter traveling in a semicircle. (a) What is the mass-to-charge ratio of the particle? (b) What is the mass of the particle if it is doubly ionized? (c) What is its identity, assuming it’s an element?

a)

To determine
The mass to charge ratio of the particle.

Explanation

Given info: The electric field between the plates of the velocity selector has a magnitude of 8250â€‰Vâ‹…m-1 . The magnetic fields in both the velocity selector and thr deflection chamber have magnitude of 0.0931â€‰T . In the deflection chamber the particle strikes a photographic plate 39.6â€‰cm removed from its exit point after travelling in a semicircle.

Explanation:

The velocity of the particle coming out of the velocity selector is,

v=EB (1)

• E is the electric field
• B is the magnetic field

Since the magnetic field supplies the centripetal acceleration,

qvB=mv2r

• B is the magnetic field present
• v is the velocity
• q is the charge of the particle
• r is the radius of the circular path
• m is the mass of the particle

Re-arranging for the ratio of mass to charge,

mq=rBv

Using (1) the mass to charge ratio will be,

mq=rB(EB)=B2(2r)2E=B2d2E

• d is the diameter of the circular path

Substitute 8250â€‰Vâ‹…m-1 for E , 0

b)

To determine
The mass of the particle if it is doubly charged.

c)

To determine
The identification of the particle assuming it is an element.

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