Separation anxiety Uranium has three stable isotopes Over 99% of naturally occur

Question

Separation anxiety Uranium has three stable isotopes Over 99% of naturally occurring uranium is ^235U, about 0.7% is and a very small amount is ^234U. During WWII, there was a tremendous push to separate out the ^235U for use in nuclear weapons. Much of the uranium was produced in a scaled up version of a mass spectrometer. Samples of uranium were ionized by removing one election. The ions were accelerated to a uniform speed, then were sent into a region of uniform 0.25 T field where they followed semicircular paths of varying radius. There arc three beams noted in the diagram above. labeled 1. 2 and 3. In order, beams 1. 2 and 3 correspond to what isotopes? A single atom or ^235U has a mass of approximately 235 u To what approximate speed should the ^235U ions he accelerated to land in the collector alter traversing the 0.25 T field region?

Explanation / Answer

Here,

1) as the radius of the trajectory of ions is given as

r = m * v/(B * q)

hence , the radius of path is directly proporational to mass of ion

path 1 is U-234

path 2 is U -235

path 3 is U-238

the correct option is B) 234 - U , 235 -U , 238 -U

2)

magnetic field , B = 0.25 T

radius of loop , r =2.4/2 m = 1.2 m

let the speed of the ion is v

Using radius = m * v/(B*q)

1.2 = 235 * 1.67 *10^-27 * v/(0.25 * 1.602 *10^-19)

solving for v

v = 125 000 m/s

the speed of the ions is A) 125000 m/s

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