A mass spectrometer can separate ions according to their charges and masses. One
ID: 1324518 • Letter: A
Question
A mass spectrometer can separate ions according to their charges and masses. One simple design for such a device is shown in the figure below. Ions of mass m, charge q, and speed v enter a region in which the magnetic field B is constant and perpendicular to the plane. The ions then travel in a circular arc and leave the spectrometer a distance L = 2r from their entry point. Consider a hypothetical mass spectrometer used to study the isotopes of hydrogen. Find r for H+, D+ (deuterium), and T+ (tritium). (Assume each particle has an incoming velocity v = 4.3 105 m/s and that the magnetic field perpendicular to the plane is B = 0.71 T. Note: H+ contains 1 proton and no neutrons, D+ contains 1 proton and 1 neutron, and T+ contains 1 proton and 2 neutrons.)
A mass spectrometer can separate ions according to their charges and masses. One simple design for such a device is shown in the figure below. Ions of mass m, charge q, and speed v enter a region in which the magnetic field B is constant and perpendicular to the plane. The ions then travel in a circular arc and leave the spectrometer a distance L = 2r from their entry point. Consider a hypothetical mass spectrometer used to study the isotopes of hydrogen. Find r for H+, D+ (deuterium), and T+ (tritium). (Assume each particle has an incoming velocity v = 4.3 105 m/s and that the magnetic field perpendicular to the plane is B = 0.71 T. Note: H+ contains 1 proton and no neutrons, D+ contains 1 proton and 1 neutron, and T+ contains 1 proton and 2 neutrons.)Explanation / Answer
The ion os moving in a circular motion due to external magnetic field
m v^2 / r = B q v
r = m v / B q
For H +
r = ( 1. 67*10^ -27 kg ) ( 4.3*10^ 5 m/s ) / ( 0.71 T) ( 1.6*10^ -19 C)
= 0.0063 m
For D+
r = 2( 1. 67*10^ -27 kg ) ( 4.3*10^ 5 m/s ) / ( 0.71 T) ( 1.6*10^ -19 C)
= 0.0126 m
For T+
r = 3( 1. 67*10^ -27 kg ) ( 4.3*10^ 5 m/s ) / ( 0.71 T) ( 1.6*10^ -19 C)
= 0.018 m
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