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

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In summary, the problem asks for the mass of an ion that is accelerated by a voltage of 2.00 kilovolts and then bends into a circular path in a uniform magnetic field of 0.400 T with a radius of 0.305 m. The equation used is m = (qB^2r^2)/2V, and after some calculation, the mass is found to be -5.96x10^-22 kg. However, this is incorrect as the charge should be positive (+e) instead of negative. The correct mass is 1.67x10^-27 kg.
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shimizua
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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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  • #3
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?
 
  • #4
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
 
  • #5
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.
 

1. What is an ion?

An ion is an atom or molecule that has gained or lost one or more electrons, resulting in a positive or negative charge.

2. How is ion mass measured?

Ion mass is measured using a mass spectrometer, which separates ions based on their mass-to-charge ratio and then measures their mass.

3. What is the unit of ion mass?

The unit of ion mass is the atomic mass unit (amu) or Dalton (Da). It is defined as 1/12 of the mass of a carbon-12 atom.

4. Why is the mass of an ion different from the mass of the atom it originated from?

The mass of an ion is different from the mass of the atom it originated from because the ion has gained or lost electrons, which changes its overall mass.

5. How does the mass of an ion affect its behavior in chemical reactions?

The mass of an ion can affect its behavior in chemical reactions as it determines its charge and how it interacts with other ions and molecules. Heavier ions may have a lower reactivity due to their greater mass and slower movement.

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