College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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![**Transcription for Educational Website**
**Mass Spectrometer Explanation**
The image illustrates a mass spectrometer, an analytical instrument used to identify various molecules in a sample by measuring their charge-to-mass ratio \( q/m \). The sample is ionized, and the positive ions are accelerated (starting from rest) through a potential difference \( \Delta V \). 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 gradually 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.
**Diagram Description**
The figure shows the trajectory of ions in the mass spectrometer. Ions are accelerated by a potential difference \( \Delta V \) and then bent into circular paths by a magnetic field. The path includes a section marked as \( d \), which leads to the detector positioned at the end of the trajectory.
**Part B**
What accelerating potential difference \( \Delta V \) is required to detect \( N_2^+ \)?
_Express your answer to five significant figures and include the appropriate units._
\[
\Delta V_{N_2^+} = \boxed{\text{Value}} \text{ Units}
\]
**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 \( \Delta V \) is required to detect \( CO^+ \)?
_Express your answer to five significant figures and include the appropriate units._
\[
\Delta V_{CO^+} = \boxed{\text{Value}} \text{ Units}
\]](https://content.bartleby.com/qna-images/question/41ab191e-c073-40ce-8516-ced92bd98c65/32f24897-18c4-40ce-8108-ba570c5c7ef3/f8zh7ju_processed.jpeg)
Transcribed Image Text:**Transcription for Educational Website**
**Mass Spectrometer Explanation**
The image illustrates a mass spectrometer, an analytical instrument used to identify various molecules in a sample by measuring their charge-to-mass ratio \( q/m \). The sample is ionized, and the positive ions are accelerated (starting from rest) through a potential difference \( \Delta V \). 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 gradually 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.
**Diagram Description**
The figure shows the trajectory of ions in the mass spectrometer. Ions are accelerated by a potential difference \( \Delta V \) and then bent into circular paths by a magnetic field. The path includes a section marked as \( d \), which leads to the detector positioned at the end of the trajectory.
**Part B**
What accelerating potential difference \( \Delta V \) is required to detect \( N_2^+ \)?
_Express your answer to five significant figures and include the appropriate units._
\[
\Delta V_{N_2^+} = \boxed{\text{Value}} \text{ Units}
\]
**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 \( \Delta V \) is required to detect \( CO^+ \)?
_Express your answer to five significant figures and include the appropriate units._
\[
\Delta V_{CO^+} = \boxed{\text{Value}} \text{ Units}
\]
Expert Solution
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Step 1
When the electron enters the magnetic field, the magnetic force is equal to the centripetal force.
Apply the work-energy theorem and substitute the required expression for the velocity to obtain the expression for the potential difference.
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