The figure(Figure 1) shows a mass spectrometer, an analytical instrument used to

Question

The figure(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 ?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 mT magnetic field and an 8.0000 cm spacing between the entrance and exit holes.

Part A

To five significant figures, what accelerating potential difference ?V 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. 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. Use the following constants: 1 u = 1.660510?27kg, e = 1.602210?19C.

Atomic masses

Express your answer to five significant figures and include the appropriate units.

(1) VO+2 =

There are the answers I tried. All wrong.

96.5V

43244V

49395V

96.519V

(2) VCO+ = ?

12C 12.000 u 14N 14.003 u 16O 15.995 u The figure(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 ?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 mT magnetic field and an 8.0000 cm spacing between the entrance and exit holes. Part A To five significant figures, what accelerating potential difference ?V 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. 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. Use the following constants: 1 u = 1.6605½10?27kg, e = 1.6022½10?19C. Atomic masses 12C 12.000 u 14N 14.003 u 16O 15.995 u Express your answer to five significant figures and include the appropriate units. (1) VO+2 = There are the answers I tried. All wrong. ?VO+2 = 96.5V ?VO+2 = 43244V ?VO+2 = 49395V ?VO+2 = 96.519V (2) VCO+ = ?

Explanation / Answer

The basic equations are:

- Calculation of speed: (m/2)v^2 = qV, or v = sqrt( (2q/m)*V)

- In a magnetic field B, the force on charge q is
F = q(v/c)B
Since it travels in a circle of radius r,
F = (m/r)v^2

So:
qvB/c = mv^2/r
or
r = vc/(qB)

- Therefore,
r = (c/qB) v = (c/qB) sqrt( (2q/m)*V)

or
V = m (q/2)(Br/c)^2
= m (q/2)(Bd/(2c))^2

where:
q = electron charge in Coulombs
B = 0.2 Tesla
d = 0.8 m
c = 3e8 m/s
m = mass of the ion in kg:

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