PLEASE HELP!! I did the problem and got 8.103 cm as the answer, but I\'m not sur

Question

PLEASE HELP!! I did the problem and got 8.103 cm as the answer, but I'm not sure if this is correct.

One way in which Uranium 235 was separated from Uranium 238 in World War 2 was to use a mass spectrograph to separate the 2 isotopes. Suppose the uranium atoms are ionized so that they have a net charge of +2 elemental charge units. These ions are then accelerated through a constant electric field of 204 N/C for 52 centimeters in a constant magnetic field. The constant magnetic field is produced by a solenoid with 170 coils per meter wrapped around a cylinder with 5.4 Amps of current running through it. The two ions have different paths through the magnetic field into 2 different containers as in the diagram below. How far apart, d in centimeters, do the centers of the containers have to be to maximize collecting both isotopes?

Explanation / Answer

apply the relation betweeb eelctric field and magnetic field as E = Bc

also E = V/d

V   = 204*0.52

V = 106.08 Volts

use KE = PE

v^2 = 2e V/m

v^2 = 2*1.6 e-19 * 106.08/9.11 e-31

v =   6.1 e 6 m/s

so B = E/v = 204/6.1 e 6   = 3.344 e -5 Tesla

so now use B = N uo i /2pi R

so

R = (170 * 4*3.14 e-7 * 5.4)/(2 *3.14 * 3.344 e-5)

R = 5.49 cm

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