Uranium has two isotopes of masses 235 and 238 units. If both of them are present in uranium hexafluoride gas, find the percentage ratio of difference in rms velocities of two isotopes to the rms velocity of heavier isotope.

Options

A. 1.64
B. 0.064
C. 0.64
D. 6.4

Answer

C

Explanation

First Uranium isotope mass, `m=238`
Second Uranium isotope mass, `m_2=235`
`v_(rms) alpha(1)/(sqrt(m))`
Percentage ratio of difference in velocity is, `(V_(rms_2)-V_(rms_1))/(V_(rms_2))xx100`
`=(sqrt(m_1)-sqrt(m_2))/(sqrt(m_2))xx100`
`=(sqrt(238)-sqrt(245))/(sqrt(238))xx100`
`=(15.42-15.329)/(15.427)xx100`
`=(0.097)/(15.427)xx100`
`=6.34xx10^(-3)xx100=6.34xx10^(-1)`
`0.63 approx 0.64`.