Question

There are two important isotopes of uranium— 235U and 238U; these isotopes are nearly identical chemically but have different atomic masses. Only 235U is very useful in nuclear reactors. One of the techniques for separating them (gas diffusion) is based on the different average velocities vrms of uranium hexafluoride gas, UF6. (a) The molecular masses for 235UUF6 and 238UUF6 are 349.0 g/mol and 352.0 g/mol, respectively. What is the ratio of their average velocities?

Answer 1

1.0043

Step-by-step explanation:

The formula for root mean square velocity is:

`V_(rms)=\sqrt {\frac {3* R* T}{M}}`

Where,

R is the universal gas constant

T is the temperature

M is the molecular weight

Since, seen from the formula, root mean square velocity is inversely proportional to the square root of the molecular mass.

Thus, for two gases like
`^(235)U\ UF_6\ and\ ^(238)U\ UF_6`.The expression is:

`\frac {{V_(rms)}_(^(235)U\ UF_6)}{{V_(rms)}_(^(238)U\ UF_6)}=\sqrt {\frac {M_(^(238)U\ UF_6)}{M_(^(235)U\ UF_6)}}`

The molecular mass of
`^(235)U\ UF_6` is 349.0 g/mol

The molecular mass of
`^(238)U\ UF_6` is 352.0 g/mol

`\frac {{V_(rms)}_(^(235)U\ UF_6)}{{V_(rms)}_(^(238)U\ UF_6)}=\sqrt {\frac {352}{349}}`

`\frac {{V_(rms)}_(^(235)U\ UF_6)}{{V_(rms)}_(^(238)U\ UF_6)}=1.0043`