Question

Uranium has two isotopes of masses $235$ and $238$ units. If both of them are present in Uranium hexafluoride gas, which have the larger average speed ? If atomic mass of fluorine is $19$ units, estimate the percentage difference in speeds at any temperature.
How is the above concept of difference in speeds utilised in the enrichment of uranium needed for nuclear fission ?

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

Answer 1

Answer: (C)

$0.64$

Rms velocity is given by $V_{rms}=\sqrt{\frac{3RT}{M}}$
$⟹$ $V_{rms}=\propto \frac{1}{\sqrt{M}}$
Given : $M_1=235amu$ and $M_2=238amu$
$⟹$ $\frac{V_1}{V_2}=\sqrt{\frac{M_2}{M_1}}$
$\therefore$ $\frac{V_1}{V_2}=\sqrt{\frac{238}{235}}=1.0064$
Or $V_1=1.0064V_2$
Percentage ratio $=\frac{V_1-V_2}{V_2}\times 100=\frac{1.0064-1}{1}\times 100=0.64$