The image below shows a mass spectrometer, an analytical instrument used to iden

Question

The image below shows a mass spectrometer, an analytical instrument used to identify the various molecules in a sample by measuring their charge-to-mass ratio e/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. Typical design values are a magnetic field strength B = 0.624 T and a spacing between the entrance and exit holes d = 8.92 cm.

What accelerating potential difference ?V is required to detect O2+?

What accelerating potential difference ?V is required to detect CO+?

Explanation / Answer

For O2 its mass is 32(1.66053892 X 10-27) = 5.313 X 10-26 kg

r = mv/qB

(.0446) = (5.313 X 10-26)(v)/(1.6 X 10-19)(.624)

v = 83811 m/s

Then PE = KE

qV = .5mv2

(1.6 X 10-19)(V) = (.5)(5.313 X 10-26)(83811)2

V = 1166 V

For the CO atom mass is (12.01 + 16)(1.66053892 X 10-27) = 4.319 X 10-26 kg

r = mv/qB

(.0446) = (4.319 X 10-26)(v)/(1.6 X 10-19)(.624)

v = 103099 m/s

Then PE = KE

qV = .5mv2

(1.6 X 10-19)(V) = (.5)(4.319 X 10-26)(103099)2

V = 1435 V

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