(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 AV, 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 a 200.00 mT magnetic field and an 8.0000 cm spacing between the entrance and exit holes. Figure + AV E Detector < 1 of 1 ♥ Submit Part B What accelerating potential difference AV is required to detect N₂ ? Express your answer to five significant figures and include the appropriate units. AVN; = Submit Part C Request Answer AVCO+ = Submit HA Value Request Answer Although N 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 AV is required to detect CO+? Express your answer to five significant figures and include the appropriate units. μÃ Value → Request Answer Units d [>] ? Units 3) ? +

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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(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 AV, 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 a
200.00 mT magnetic field and an 8.0000 cm spacing
between the entrance and exit holes.
Figure
+
AV
11.1
Detector
.
•
1 of 1
Submit Request Answer
Part B
What accelerating potential difference AV is required to detect N?
Express your answer to five significant figures and include the appropriate units.
AVN
=
Submit
Part C
AVCot
Submit
HÅ
=
Value
Request Answer
Although N 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 AV is required to detect CO?
Express your answer to five significant figures and include the appropriate units.
μÀ
Value
Units
Request Answer
□】?
Units

Expert Solution

Step 1

When the electron enters the magnetic field, the magnetic force is equal to the centripetal force.

$\begin{array}{l} F_{M} = F_{C} \\ q v B = \frac{m v^{2}}{r} \\ v = \frac{q B r}{m} \end{array}$

Apply the work-energy theorem and substitute the required expression for the velocity to obtain the expression for the potential difference.

$\begin{array}{l} W = Δ K E \\ q (Δ V) = \frac{1}{2} m v_{f}^{2} - \frac{1}{2} m v_{i}^{2} \\ q (Δ V) = \frac{1}{2} m {(\frac{q B r}{m})}^{2} - \frac{1}{2} m {(0)}^{2} \\ Δ V = \frac{q B^{2} r^{2}}{2 m} \end{array}$

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