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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+ ________V

Explanation / 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

-----------------------------------------------------------------------------------------------

(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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