The 235 U isotope (atomic mass = 235.00) undergoes fission when bombarded with n

Question

The 235 U isotope (atomic mass = 235.00) undergoes fission when bombarded with neurons. However, its natural abundance is only 0.72 percent. To seperate it from the more abundant 238 U isotope (atomic mass = 238.00), uranium is first converted to UF6, which is easily vaporized above room temperature. The mixture of 235 UF6 and 238 UF 6 gases is then sunjected to many stages of effusion. Calculate how much more quickly 235 UG6 effuses than 238 UF6. Give the answer as the ratio of rates of 235 UF6 to 238 UF6 to four decimal places.

Explanation / Answer

We know rate of effusion is inversely proportional to the square root of the molar mass.

And when we have to compare the rate of effusion we use the ratio of molar mass as follow.

Rate 1 / Rate 2 = ( sqrt( Molar mass of 2) / sqrt ( molar mass of 1))

We know that the U-235 has low molar mass than U-238 so Lets use Rate 1 for U-235 and Rate 2 = U-238

We also need to find molar masses of UF6

( use molar mass of F = 18.998 g/mol

Molar mass of U(235)F6 = 235 + ( 6 x 18.998) = 348.998

Molar mass of U(238)F6 = 238 + (6 x 18.998) = 351.998

Lets plug in the values to get ratio

Rate ( U(235)F6) / Rate ( U(238)F6) = ( sqrt (351.998)/sqrt (348.998))

=1.0043

So the rate of U-235 is diffuses 1.0043 times faster than U-238

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