Question

(Figure 1) 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 ΔV, 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.

+ AV - Detector

To five significant figures, what accelerating potential difference ΔV is required to detect the ion O+2? The masses of the atoms are shown in the table; the mass of the missing electron is less than 0.001 u and is not relevant at this level of precision. Use the following constants: 1 u = 1.6605×10−27kg, e = 1.6022×10−19C.
Atomic masses

12C   12.000 u
14N   14.003 u
16O   15.992 u
Express your answer to five significant figures and include the appropriate units.

What accelerating potential difference ΔV is required to detect N+2?

Although N+2 and CO+ both have a nominal molecular mass of 28, they are easily distinguished by virtue of their slightly different accelerating voltages. What accelerating potential difference ΔV is required to detect CO+?

Answer 1

a )

r = 8 / 2

= 4 cm

= 0.04 m

r = m v / q B

we have ΔV = r² B² q / 2 m

= 0.04² x 0.2² x q / 2 m

ΔV = 32 x 10^-6 ( q/m )

ΔV _O2+ = 32 x 10^-6 x 1.6 x 10^-19 / 2 x 15.992 x 1.67 x 10^-27

ΔV _O2+ = 96.537 volts

b )

ΔV _N2+ = 32 x 10^-6 x 1.6 x 10^-19 / 2 x 14.003 x 1.67 x 10^-27

ΔV _O2+ = 110.249 volts

c )

ΔV _CO+ = 32 x 10^-6 x 1.6 x 10^-19 / ( 12 + 15.992 ) x 1.67 x 10^-27

ΔV _CO+ = 110.3046 volts