A. Two ions with masses of 8.8 × 1027 kg move out of the slit of a mass spectrom

Question

A. Two ions with masses of 8.8 × 1027 kg move out of the slit of a mass spectrometer and into a region where the magnetic field is 0.165 T. Each has a speed of 1.19 × 106 m/s, but one ion is singly charged and the other is doubly charged. Find the radius of the circular path followed by the singly charged ion in the field. Answer in units of cm.

B. Find the radius of the circular path followed by the doubly charged ion in the field. Answer in units of cm.

C. Find the distance of separation when they have moved through one-half of their circular path and strike a piece of photographic paper. Answer in units of cm.

Explanation / Answer

centripetal force = mv^2/r

megnetic force = qvB

now, centripetal force = megnetic force

=> mv^2/r = qvB

=> r = mv/qB

A singly charged ion has a charge of e = 1.6*10^(-19)

=> r = 8.8*10^(-27)*1.19*10^6/(1.6*10^(-19)*0.165) = 0.397 m

r = 39.7 cm

B)

A double charged ion has a charge of 2e = 2*1.6*10^(-19)

r2 = mv/qB

r2 = 8.8*10^(-27)*1.19*10^6/(2*1.6*10^(-19)*0.165) = 0.1985 m

C)

Their distance of separation after one-half their circular path is d = 2 ( r1 r2 ) = 2*(0.397 m 0.1985 m) = 0.397 m

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