The figure below shows a mass spectrometer, an analytical instrument used to ide
ID: 1287665 • Letter: T
Question
The figure 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 = 0.390 T and a spacing between the entrance and exit holes d = 8.40 cm. What accelerating potential difference V is required to detect the following? (Use e = -1.60218 10^-19 C for the charge of an electron, and u = 1.66054 10^-27 kg for atomic mass. Round your answers to six significant figures.)
______ V
Atomic masses 12C 12.0000 u 14N 14.0031 u 16O 15.9949 u The figure 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 = 0.390 T and a spacing between the entrance and exit holes d = 8.40 cm. What accelerating potential difference V is required to detect the following? (Use e = -1.60218 10^-19 C for the charge of an electron, and u = 1.66054 10^-27 kg for atomic mass. Round your answers to six significant figures.) Atomic masses 12C 12.0000 u 14N 14.0031 u 16O 15.9949 u (a) N2+ ______ V (b) O2+ _______V (c) CO+ ________VExplanation / Answer
(a)
The required mass is,
mN2 = 2mN - me
= 2(14.0031 u)(1.66054x10-27 kg / 1 u) - 9.11x10-31 kg
= 4.65x10-26 kg
the expression for the potential difference is,
dV = qd2B2/ 8m
= (1.60218x10-19 C)(0.084 m)2(0.390 T)2 / 8(4.65x10-26 kg)
= 462.35 V
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(b)
The required mass is,
mO2 = 2mO - me
= 2(15.9949 u)(1.66054x10-27 kg / 1 u) - 9.11x10-31 kg
= 5.312x10-26 kg
the expression for the potential difference is,
dV = qd2B2/ 8m
= (1.60218x10-19 C)(0.084 m)2(0.390 T)2 / 8(5.312x10-26 kg)
= 404.6 V
----------------------------------------------------------------------------------------------
(c)
The required mass is,
mCO = 2mCO - me
= (12.0000 u + 15.9949 u)(1.66054x10-27 kg / 1 u) - 9.11x10-31 kg
= 4.648574x10-26 kg
the expression for the potential difference is,
dV = qd2B2/ 8m
= (1.60218x10-19 C)(0.084 m)2(0.390 T)2 / 8(4.648574x10-26 kg)
= 462.37 V
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