Homework SourseA mass spectrometer is a device that uses a magnetic field t
A mass spectrometer is a device that uses a magnetic field to sort atoms by mass. In this device, atoms whose masses are to be determined are ionized by stripping off one electron. They are then sent through a velocity selector that selects ions only with a very specific speed, and these ions are sent into a region of space filled with a known uniform magnetic field perpendicular to the velocity. The field causes each atom to follow a circular path whose radius is proportional to the atom\'s mass. Atoms with different masses will therefore follow somewhat different circular paths and thus end up at different places on a photographic plate, as shown. Imagine that we give N2+ ions, O2+ ions, and NO+ ions the same velocity of 30 km/s and then send them into a mass spectrometer where the magnetic field strength is B = 8.5 MN/C. How far would the spot on the photographic plate be from the entry point for each ion, assuming that each ion completes half an orbit, as shown in the figure? The atomic mass of a nitrogen atom is 14.0031 amu and oxygen is 15.9949 amu, where 1 amu= 1.6605 x 10-27 kg.
Solution
velocity v = 30 km/s
= 30000 m/s
magnetic field strength B = 8.5 MT
= 8.5 x10 6 T
The atomic mass of a nitrogen atom m= 14.0031 amu
= 14.0031 x1.6605 x10 -27 kg
The atomic mass of oxygen m\' = 15.9949 amu
= 15.9949 x1.6605 x 10-27 kg.
In magnetic field ,force due to magnetic field = centripeatl force
Bvq = mv 2 / R
Bq = mv /R
From this radius R = mv /Bq
Where q = Charge of ion = 2x1.6 x10 -19 C
For Oxygen:
Radius R = (15.9949 x1.6605 x 10-27 )(30000)/(8.5 x10 6 )( 2x1.6 x10 -19 )
= 2.929 x10 -10 m
Distance of the oxygen from entry point = 2R = 5.858 x10 -10 m
Similarly for nitrogen,
Radius R \' = (14.0031 x1.6605 x 10-27 )(30000)/(8.5 x10 6 )( 2x1.6 x10 -19 )
= 2.5645 x10 -10 m
Distance of the notrogen from entry point = 2R \' = 5.129 x10 -10 m
