Mass Spectrograph. A mass spectrograph is used to measure the masses of ions, or to separate ions of different masses (see Section 27.5). In one design for such an instrument, ions with mass m and charge q are accelerated through a potential differ- ence V. They then enter a uniform magnetic field that is perpen- dicular to their velocity, and they are deflected in a semicircular path of radius R. A detector measures where the ions complete the semicircle and from this it is easy to calculate R. (a) Derive the equation for calculating the mass of the ion from measurements 27.60

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27.60
Mass Spectrograph. A mass spectrograph is used to
measure the masses of ions, or to separate ions of different masses
(see Section 27.5). In one design for such an instrument, ions with
mass m and charge q are accelerated through a potential differ-
ence V. They then enter a uniform magnetic field that is perpen-
dicular to their velocity, and they are deflected in a semicircular
path of radius R. A detector measures where the ions complete the
semicircle and from this it is easy to calculate R. (a) Derive the
equation for calculating the mass of the ion from measurements
of B, V, R, and q. (b) What potential difference V is needed so
that singly ionized 12C atoms will have R = 50.0 cm in a 0.150-T
magnetic field? (c) Suppose the beam consists of a mixture of 12C
and 14C ions. If v and B have the same values as in part (b), cal-
culate the separation of these two isotopes at the detector. Do you
think that this beam separation is sufficient for the two ions to be
distinguished? (Make the assumption described in Problem 27.59
for the masses of the ions.)
Transcribed Image Text:27.60 Mass Spectrograph. A mass spectrograph is used to measure the masses of ions, or to separate ions of different masses (see Section 27.5). In one design for such an instrument, ions with mass m and charge q are accelerated through a potential differ- ence V. They then enter a uniform magnetic field that is perpen- dicular to their velocity, and they are deflected in a semicircular path of radius R. A detector measures where the ions complete the semicircle and from this it is easy to calculate R. (a) Derive the equation for calculating the mass of the ion from measurements of B, V, R, and q. (b) What potential difference V is needed so that singly ionized 12C atoms will have R = 50.0 cm in a 0.150-T magnetic field? (c) Suppose the beam consists of a mixture of 12C and 14C ions. If v and B have the same values as in part (b), cal- culate the separation of these two isotopes at the detector. Do you think that this beam separation is sufficient for the two ions to be distinguished? (Make the assumption described in Problem 27.59 for the masses of the ions.)
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