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23 February, 21:31

A mass spectrometer, sketched, is a device used to separate different ions. Such ions with a well-defined velocity vo enter through a slit into a region of uniform magnetic field B, where they follow a semicircular path until they strike the detector slit above the entry slit. The distance between the entry and the detector slits is d = 1.20 m.

Chlorine ions of mass 35 amu (1 amu equals 1.66x10-27 kg), carrying a charge of + 1e, enter the spectrometer with initial speed of vo = 8.70E5 meters/sec. What value of B is required for these ions to hit the detector?

Equally charged chlorine ions of mass 37 amu now enter the spectrometer. How close to the detector slit will they impact?

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  1. 24 February, 00:53
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    From the given data, it appears that, the ion particles are moving on a circular path of radius 1.2 / 2 = 0.6 m in the magnetic field.

    In the circular path, centripetal force is provided by magnetic force on ions

    m v² / R = Bq v

    B = mv / q R

    = 35 x 1.66 x 10⁻²⁷x 8.7 x 10⁵ / 1.6 x 10⁻¹⁹ x. 6

    = 526.53 x 10⁻³ T.

    If mass of the ion becomes 37 x 1.66 x 10⁻²⁷, the radius of circular path will be changed

    m v² / R = Bq v

    R = mv / qB

    37 x 1.66 x 10⁻²⁷ x 8.7 x 10⁵ / 1.6 x 10⁻¹⁹ x 526.53 x 10⁻³

    =.634 m

    difference =.634 -.6

    .034 m

    = 3.4 cm

    The ion will hit 3.4 cm away from the detector.
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