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

Given,
Mass of first uranium isotope = 238 units
Mass of second uranium isotope = 235 units
We know that,
`V_(rms) = sqrt((gamma RT)/(M))`
`implies V_(rms) prop (1)/(sqrt(M))`
So, the percentage ratio of difference in ms velocity of isotopes is given by
`(V_(rms_(2)) - V_(rms_(1)))/(V_(rms_(2))) xx 100`
`= (sqrt(M_(1)) - sqrt(M_(2)))/(sqrt(M_(1))) xx 100`
`= (sqrt(238) - sqrt(235))/(sqrt(238)) xx 100`
`= (15.427 - 15.329)/(15.427) xx 100 = (0.097)/(15.427) xx 100`
`= 6.34 xx 10^(-3) xx 100 = 0.634 = 0.64`