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?

Question

Physics

Brogan Hunter

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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Answers (1)

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Benson · Answer 1

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.