One way in which Uranium 235 was separated from Uranium 238 in World War 2 was t

Question

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 each have a net charge of +2 elemental charge units. These ions are then accelerated through a constant electric field of 102 N/C for 2/3 centimeters m a constant magnetic field. The constant magnetic field is produced by a solenoid with 2308 coils per meter wrapped around a cylinder with 45.7 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? Give your answer in centimeters to 1 decimal place.

Explanation / Answer

apply the relation between electric field and Potnetail as E = V/d

so

Potential V = E d

V = 102 * 0.23

V = 23.46 Volts

so now usign KE = PE

0.5 mv^2 = eV

v = sqrt(2eV/m)

here

v = sqrt(2 * 2 *1.6 e-19 * 23.46/(2 *1.67 e-27)

v = 6.7 *10^4 m/s

use the formula to find magnetic field B = uoNi

B = 4*3.14 e-7 * 2308 * 45.7

B = 0.1324 T

so now use Centripetal force = magnetic force

mv^2/r = qvB

r     = mv/qB

r = 1.67 e -27 * 6.7 e 4/(1.6 e-19 * 0.1324)

r = 5.28 mm----------------<<<<<<<<<<<<<<<<<<Answer

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