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 slit is d = 1.60 m. detector slit X X X X X X X XXX XXXXXX 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 = 6.60x10 % m/s. What value of B is required for these ions to hit the detector? 2.996x10-1 T You are correct. Previous Tries Your nois 7526 receipt . 158-e Equally charged chlorine ions of mass 37 amu now enter the spectrometer. How close to the detector slit will they impact? Since the centripetal force is the SAME for both isotopes, the more massive isotope will overshoot the detector.

Explanation / Answer

m = mass = 35 amu = 35 x 1.66 x 10-27 kg

q = charge = 1.6 x 10-19 C

B = magnetic field

v = speed = 6.6 x 105 m/s

r = radius of semicircle = d/2 = 1.60/2 = 0.8 m

using the equation

r = mv/(qB)

hence B = mv/(qr)

B = ( 35 x 1.66 x 10-27) (6.6 x 105)/((1.6 x 10-19) (0.8)) = 0.2296 T

for the 37 amu CL ion

d' = 2r' = 2m'v/(qB) = 2 (37 x 1.66 x 10-27) (6.6 x 105)/(1.6 x 10-19) (0.2296)) = 2.2 m

2.2 - 1.6 = 0.8 m close to the detector slit

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