Uranium has two isotopes of masses 235 and 238 units . If both are present in uranium hexafluoride gas which would have the larger average speed ? If atomic mass of fluorine is 19 units , estimate the percentage difference in speeds at any temperature

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Solution

At a fixed temperature, kinetic energy of gas molecules is constant. Kinetic energy is given by

Rearranging, we get
$K E equals 1 half m v squared rightwards double arrow v squared equals fraction numerator 2 cross times K E over denominator m end fraction rightwards double arrow v equals square root of fraction numerator 2 cross times K E over denominator m end fraction end root rightwards double arrow v space alpha space fraction numerator 1 over denominator square root of m end fraction$

Therefore, smaller the mass of molecule, higher will be its speed.

The masses of the 2 types of uranium hexafluorides are

Therefore, the U-235 hexafluoride is faster.

Taking the ratios of their velocity
$v subscript 235 over v subscript 238 equals fraction numerator begin display style fraction numerator 1 over denominator square root of 349 end fraction end style over denominator begin display style fraction numerator 1 over denominator square root of 352 end fraction end style end fraction space space space space space space space space space space equals fraction numerator square root of 352 over denominator square root of 349 end fraction space space space space space space space space space space space equals 1.0043$

Therefore, the percentage difference is 0.43%.

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