shows a mass spectrometer, an analytical instrument used to identify the various
ID: 1457642 • Letter: S
Question
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 ?V, 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.
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Explanation / Answer
radius of the orbit = m*v/(B*q)
= sqrt(2*m*KE)/(B*q)
= sqrt(2*m*q*delta_V)/(B*q)
r = sqrt(2*m*delta_V/q)/B
d = 2*r
d = 2*sqrt(2*m*delta_V/q)/B
d^2 = 4*2*m*delta_V/(q*B^2)
delta_V = d^2*q*B^2/(8*m)
so,
A) delta_V = 0.08^2*1.6022*10^-19*0.2^2/(8*2*15.992*1.6605*10^-27)
= 96.537 volts
B) delta_V = 0.08^2*1.6022*10^-19*0.2^2/(8*2*14.003*1.6605*10^-27)
= 100.25 volts
C) delta_V = 0.08^2*1.6022*10^-19*0.2^2/(8*12*1.6605*10^-27)
= 257.30 volts
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