What is the equation for finding the mass of an ion using a mass spectrometer?

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Homework Help Overview

The problem involves using a mass spectrometer to determine the mass of a singly charged ion after it has been accelerated through a voltage and enters a magnetic field, resulting in a circular path. The relevant parameters include the voltage, magnetic field strength, and radius of the path.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the equation derived from force considerations and question how to determine the charge of the ion. There is uncertainty regarding the sign of the charge and its implications for the calculation of mass.

Discussion Status

Some participants have attempted calculations using the charge of the ion, while others have pointed out the need to clarify the sign of the charge. There is ongoing exploration of the implications of using the correct value for charge in the mass calculation.

Contextual Notes

Participants are working under the assumption that the ion is singly charged and are referencing the elementary charge. There is a focus on ensuring the correct application of the charge value in the context of the mass spectrometer's operation.

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Homework Statement


A mass spectrometer applies a voltage of 2.00 kilovolts to accelerate a singly charged ion (+e). This ion then enters a region of uniform magnetic field (B= 0.400 T) which then bends the ion into a circular path of radius 0.305 m What is the mass of the ion?


Homework Equations


after breaking everything down from F=ma i got to m = (qB^2r^2)/2V


The Attempt at a Solution


well i am just unsure of how to find q. I know that V=2kV, B=.4 T, and r=.305 m. so if you can just help me with finding q. i can do that rest
 
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ok well so i tried doing the m= -1.602x10^-19(.4^2)(.305^2)/4 and got -5.96x10^-22. would it be in kg though?
 
shimizua said:
ok well so i tried doing the m= -1.602x10^-19(.4^2)(.305^2)/4 and got -5.96x10^-22. would it be in kg though?

To put it in perspective for a single proton:
Wikipedia said:
1.672621637(83)×10−27 kg
 
The conundrum you got going here is that the charge is +e, not e. SOO...in taking your big step in finally realizing that q is given as the charge +e, you can now go figure that the charge is POSITIVE (1.6*10^-19 C), not negative.
 

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