Problem 4: Mass Spectrometer
[refer to the Lab08 handout [from Lab (available on D2L)] ]

back to Problem 2
back to Lab 08

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          initial velocity = km/s  
electric field  = kV/m          magnetic field 1  = T  

mass  =  amu       charge = e;   magnetic field 2  = T  

Please wait for the animation to completely load.

-------------- ( --- question f-1 and f-2 --- ) --------------

A charged particle enters a region with a constant magnetic field B1 and a constant electric field produced by two charged plates.   If the particle is able to pass through the first region, it enters a region with only a magnetic field B2.Restart.

The Exploration demonstrates how a mass spectrometer works   Many particles might be injected into the first region.  For certain values of electric and magnetic fields only particles with a particular velocity will pass through undeflected.  By subjecting the particles to the velocity selector, we know the velocity of the particle when it enters the second region.

  1. What are the directions of the electric field and the first magnetic field?
  2. If the initial velocity is 50 km/s, the magnetic field is .2 T, the mass is 10 amu (1 amu = 1.66054 X 10-27 kg), and the charge is -1  e, what must the electric field be in order to select the 50 km/s particle?  Calculate your answer first and then test it using the animation.
  3. If you change the value of B1, is the 50 km/s particle still selected? 
  4. Return the magnetic field to its correct value and change the mass.  What do you observe?  In particular does the particle still enter the second region and what does its trajectory look like?  Change the charge and answer the same questions. Explain.
  5. Once you are able to select the 50 km/s particle and it passes into a region where only the magnetic field is present, it follows a curved circular path.  Why?

 For every mass, the curved path will be slightly different.  This allows you to measure the mass of an individual particle.  This is very useful, and is used to identify what atoms and molecules are present in a substance.

  1. By considering the magnetic force in the second region, develop a mathematical expression that relates the mass of the particle to the other variables.  Do not include the velocity in your expression.  You can use the condition that the particle passed through the region of electric and magnetic fields undeflected to eliminate velocity from your expression.  Your expression will also contain the radius of the circular path. 

You can measure this radius in the applet using a mouse-down (position is given in centimeters).  In a real mass spectrometer the detector is placed at a known radius of curvature.  As the magnetic field in the second region is swept through its range, different masses hit the detector.  The signal strength of the detector is plotted as a function of the magnetic field, which indicates the masses of each particle and their relative abundance.

  1. Calculate the mass that will go in a 10 cm radius circle at 50 km/s, .1 Tesla for B2 and +1 e charge. Convert this to atomic mass units and enter the numbers to check your answer. 

    What magnetic field is required for singly ionized methanol (CH3OH), traveling at the same velocity,  to hit at the same spot?

 

 

Exploration authored by Melissa Dancy, with minor changes by Lyndon Zink.
? 2004 by Prentice-Hall, Inc. A Pearson Company