Uranium has three stable isotopes. Over 99% of naturally occurring uranium is 23

Question

Uranium has three stable isotopes. Over 99% of naturally occurring uranium is 238U, about 0.7% is 235U, 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.

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?

A. 238U, 235U, 234U

B. 234U, 235U, 238U

C. 235U, 234U, 238U

D. 238U, 234U, 235U

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

B. 150,000 m/s

C. 175,000 m/s

D. 200,000 m/s

Explanation / Answer

a) mass is proportional to square of radius of semicircle in mass spectroscopy.

So for larger mass radius will be large.

So, 234U, 235U, 238U (option B is correct)

b) radius = 1.2 m

velocity = v = Bqr/m = (0.25*1.6*10^-19*1.2)/(235*1.66x10-27) = 123045.4 m/s (Option A)

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