A mass spectrometer, sketched below, Is a device used to separate different lons

Question

A mass spectrometer, sketched below, Is a device used to separate different lons. Such lons with a well-deflned velocity vo enter through a slit Into a reglon of unlform magnetic fleld 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 2.00 m. Chlorine lons of mass 35 amu (1 amu equals 1.66x102 kg), carrylng a charge of +1e enter the spectrometer with Initial speed of v4.10x10 m/s. What value of B is required for these lons to hit the detector? In T) A: 9.528x102 CB:1.191×10-11-c: 1.485x 10? C D: 1.861x101||C E: 2.326 x 10-11 E 2.908x 101le G: 3.635x Eaually charged chlorine lons of mass 37 amu now enter the spectrometer. How close to the detector slit wl they Impact? (in m) A: 7.314x10 ? B: 9.143×10-2Lci 1.143x10-11 E: 1.786x10 OF: 2.232 2x10 G: 2.790x10OH: 3.488x1 D: 1.429x Tries 0/2

Explanation / Answer

Equating Magnetic force with centripetal force,
Bqv = mv2/r
Where B is the magnetic field, q, v and m are the charge, velocity and mass of the ions and r is the radius of the circular path.
B = mv/rq
m = 35 x 1.66 x 10-27 kg = 58.1 x 10-27 kg
v = 4.10 x 105 m/s
r = 1m
q = 1.6 x 10-19 C
Substituting,
B = [(58.1 x 10-27) x (4.10 x 105)]/[(1.6 x 10-19) x 1]
= 1.489 x 10-1 T (option C)

b)
Radius of circular path, r = mv/Bq
m becomes m = 37 x 1.66 x 10-27 kg = 61.42 x 10-27 kg
Substituting,
r = [(61.42 x 10-27) x (4.10 x 105)]/[(1.6 x 10-19) x (1.489 x 10-1)]
= 1.057 m

Difference = 2r - d
= 0.1143 m     (option C)

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