A mass spectrometer, sketched below, is a device used to separate different ions

Question

A mass spectrometer, sketched below, 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 slitis d = 1.00 m. detector slit Chlorine ions of mass 35 amu (1 amu equals 1.66x10kg), carrying a charge of +1e enter the spectrometer with initial speed of vo 9.60x105 m/s. What value of B is required for these ions to hit the detector? Submit Answer Tries 0/5 Equally charged chlorine ions of mass 37 amu now enter the spectrometer. How close to the detector slit will they impact? Sutomit Answer Tries o/5

Explanation / Answer

Topic in discussion: Charge particle in Uniform Magnetic Field in circular motion

The relationship in the case is of charge (q), velocity(v), mass(m), magnetic field (B) and diameter ( d = 2R)

Force on charge due to B = centripetal force on charge

qvB = mv2/R

=> B = mv / qR

= (35*1.66*10-27)(9.6*105 )/ (1.6*10-19)(0.5)

= 1.11552= 1.116 T (First Answer)

R = mv / qB

= (37*1.66*10-27)(9.6*105) / (1.6*10-19)(1.116)

= 0.33 m = 33 cm

The distance from detector will be = 1 m - 2*0.33m

= 0.34 m

= 34 cm (Second Answer)

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