1.

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

Answer» At a fixed temperature ,
average `K.E.//"molecul e"= 1/2 m upsilon^(2)= 3/2 K_(B)T`
= constat
`:. 1/2 m_(1) upsilon_(1)^(2) = 1/2 m_(2) upsilon_(2)^(2) or (upsilon_1)/(upsilon_2) = sqrt((m_2)/(m_1))`
Clearly, smaller the mass of the molecule, larger will be its average speed.
For Uranium (235) hexafluoride,
`m_(1)= 235 + 6 xx 19 = 349` units and
for Uranium (238) hexafluoride,
`m= 238 + 6 xx 19 = 352` units
`U-235` hexafluoride will have larger average speed.
`:. (upsilon_1)/(upsilon_2) = sqrt((352)/(349)) = 1/0044`
`%` age difference `=(1.0044 - 1)/(1) xx 100`
`= 0.44%`.


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