(Figure 1) shows a mass spectrometer, an analytical instrument used to identify
ID: 1422859 • Letter: #
Question
(Figure 1) shows a mass spectrometer, an analytical instrument used to identify the various molecules in a sample by measuring their charge-to-mass ratio q/m. The sample is ionized, the positive ions are accelerated (starting from rest) through a potential difference V, and they then enter a region of uniform magnetic field. The field bends the ions into circular trajectories, but after just half a circle they either strike the wall or pass through a small opening to a detector. As the accelerating voltage is slowly increased, different ions reach the detector and are measured. Consider a mass spectrometer with a200.00 mT magnetic field and an 8.0000 cm spacing between the entrance and exit holes.
Part A
To five significant figures, what accelerating potential difference V is required to detect the ion O+2? The masses of the atoms are shown in the table; the mass of the missing electron is less than 0.001 u and is not relevant at this level of precision. Use the following constants: 1 u = 1.6605×1027kg, e = 1.6022×1019C.
Atomic masses
Express your answer to five significant figures and include the appropriate units.
VO+2 = -------- V
Part B
What accelerating potential difference V is required to detect N+2?
Express your answer to five significant figures and include the appropriate units.
-------- V
Part C
Although N+2 and CO+ both have a nominal molecular mass of 28, they are easily distinguished by virtue of their slightly different accelerating voltages. What accelerating potential difference V is required to detect CO+?
Express your answer to five significant figures and include the appropriate units.
12C 12.000 u 14N 14.003 u 16O 15.992 uExplanation / Answer
from the conservation of energy
1/2 m v^2 = q delV
v = sqrt 2q delV/ m
the diameter of path is
r = mv/ qB
d/2 = mv/ qB
d = 2mv/ qB
d = 2m/ qB * sqrt 2q delV/ m
d^2 = 8 m del V/ qB^2
del V = qB^2 d^2/ 8 m
voltage diffrence across O+2 ion
del V = ( 1.6022* 10^-19 C) ( 200* 10^-3 T)^2 ( 8.0* 10^-2 m)^2/ 8 ( 2( 15.992) ( 1.6605 * 10^-5 kg)
=96.5 V
voltage diffrence across N+2 ion
del VN = del V0 ( m ( nitogen)/ m ( oxygen)
= 96.560 ( 2 ( 14.0031/ 2( 15.992)
= 84.5 V
for CO+
del V co = del Vo ( m ( co)/ m( o2)
= 96.5( 15.9949 + 12/2( 15.9949)
= 84.466 V
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