Past Exam Problem Separation Anxiety Uranium has three stable isotopes. Over 99%

Question

Past Exam Problem Separation Anxiety Uranium has three stable isotopes. Over 99% of naturally occurring uranium is 238U, about 0.7% i,asU, 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 electron. 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. 24 m Collector 1) There are three beams noted in the diagram above, labeled 1, 2 and 3. In order, beams 1, 2 and 3 correspond to what isotopes? B. 23 U, 235U, 23U A 23U, 2U230 C. 23SU, 234U, 238U 2) A single atom of 235U has a mass of approximately 235 u. To what approximate speed should the 235U ions be accelerated to land in the collector after traversing the 0.25 T field region? A 125,000 m's C. 175,000 m s B. 150,000 m's D. 200,000 m s

Explanation / Answer

1)
for circular path,

magnetic force = centripetal force

q v B = m v^2 / r

r = mv / qB

v, q and B are same for all the elements.

so more the mass, more is radius.

1 will be of lowest mass.

Ans(B)

2. to land in collector,

r = 2.4 /2 = 1.2 m

qvB = mv^2 / r

q r B = mv

1.6 x 10^-19 x 1.2 x 0.25 = (235 x 1.67 x 10^-27 kg ) v

v = 1.25 x 10^5 m/s

Ans ( A)

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