Suppose the electric field between the electric plates in the mass spectrometer

Question

Suppose the electric field between the electric plates in the mass spectrometer shown below is 2.10 104 V/m and the magnetic fields B = B' = 0.40 T. The source contains carbon isotopes of mass numbers 12, 13, and 14 from a long-dead piece of a tree. (To estimate atomic masses, multiply by 1.67 10-27 kg.)

(a) How far apart are the lines formed by the singly charged ions of each type on the photographic film? in m

(b) What if the ions were doubly charged? in m

Explanation / Answer

1. first of all, in order to cause isotopes to move on straight line between s1 to s2, following should come true: qvB=qE --> v=E/B 2. The force on isotopes in magnetic filed is F=qvB'=qvB 3. The radius of isotopes in magnetic filed is: R=mv/qB'=mE/qBB'=mE/qB^2 then, R12=12*1.67e-27*2.1e4/1.6e-19*0.4^2=0.0164 m R13=0.0178m R14=0.0192 m they will be 0.014 meters apart b) if the ioins will have double charge then the distance between the lines will be half 0.007 m

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