the atoms collide head-on. What are (a) the
magnitude and (b) the direction of the
magnetic field?
(a) T
(b) i. Positive x
ii. Negative x
iii. Positive y
iv. Negative y
v. Positive z
vi. Negative zSection 15 - Physics at work: mass spectrometer
15.1 Two elements whose atoms have the same mass number (the number of protons plus neutrons) are called isobars. The only
two stable isobars with mass number 58 are^58 Fe with a mass of 57.933277 u and^58 Ni with a mass of 57.935346 u
(1 u = 1.6605402×10í^27 kg). The mass spectrometer in a laboratory can resolve spatial displacements of 1.00×10í^4 m after a
particle's 180° flight. (a) If the particles are singly ionized and enter the spectrometer at 3.00×10^4 m/s, what magnetic field
strength will just allow these two isobars to be resolved? (Hint: for this problem, you must keep all of the significant figures for
the masses of the two types of atom as you work through the problem and round your answer at the end to the correct
number of significant figures. Why? Try rounding at the beginning of your work and see what happens.) (b) If you want to
increase the final distance between the isobars, should you increase or decrease the magnetic field strength?
(a) T
(b) Increase Decrease
15.2 A mass spectrometer has an adjustable magnetic field. When the magnetic field is 3.00eí2 T, a singly ionized hydrogen atom
(a proton) will strike the detector at a particular location. Suppose a triply-ionized carbon 12 atom, whose mass is by definition
12 u (where 1 u = 1.66×10í^27 kg) enters the spectrometer at the same speed as the proton. What is the strength of the
magnetic field that will cause it to strike the detector at the same location as the proton?
T
15.3 A neon atom of mass 3.82×10í^26 kg is triply ionized. That is, three electrons are stripped from the atom so that its charge is
+3e, or 4.80×10í^19 C. The atom is accelerated across a potential difference of magnitude 212 V, and enters a mass
spectrometer whose magnetic field has a strength of 1.25 T. (a) What is the radius of the atom's trajectory in the magnetic
field? (b) What is the radius of the trajectory of a sulfur ion, also triply ionized, but having mass 5.64×10í^26 kg? (c) What is the
distance between the points on the detector plate struck by these two atoms?(a) m
(b) m
(c) m
15.4 When the ionized particles entering a mass
spectrometer are simply accelerated across
the potential difference between two charged
plates, there is always the chance of an
uncontrolled variation in their velocities due to
their random thermal motion before they
undergo linear acceleration. An elaboration of
the basic mass spectrometer design better
controls the incoming velocity of the ions by
passing them through a velocity selector
before they enter the magnetic deflection
chamber. Suppose that the same uniform magnetic field, having a strength 0.750 T, is used in both the velocity selector and
the deflection chamber. In this chamber, singly ionized argon ions with a mass of 6.63×10í^26 kg are to be deflected through
semi-circular arcs of radius 12.0 cm. (a) If the oppositely charged plates of the velocity selector are separated by 2.00 cm,
what is the required potential difference between them? (b) If you were to add a velocity selector to the diagram of the mass
spectrometer, as shown in the illustration, which plate would be positively charged with respect to the other?
(a) V
(b) The right plate The left plate(^534) Copyright 2007 Kinetic Books Co. Chapter 28 Problems