Question

the two isotopes of uranium 238u and 235u can be separated by diffusion of the corresponding UF6 gases. what is the ratio of the root mean square speed of 238UF6 to that of 235UF6 at constant temperature

Answer 1

1.0042:1 is the ratio of the root mean square speed of
`^(238)UF_6` to that of
`^(235)UF_6` at constant temperature.

Step-by-step explanation:

The formula used for root mean square speed is:

`\\u_(rms)=\sqrt{(3kN_AT)/(M)}`

where,

`\\u_(rms)` = root mean square speed

k = Boltzmann’s constant =
`1.38* 10^(-23)J/K`

T = temperature = 370 K

M = atomic mass = 0.02 kg/mole

`N_A` = Avogadro’s number =
`6.02* 10^(23)mol^(-1)`

Root mean square speed of
`^(238)UF_6=\\u`

Molar mass of
`^(238)UF_6=M=238 g/mol+6* 19 g/mol=352 g/mol`

`\\u =\sqrt{(3kN_AT)/(M)}`

`\\u =\sqrt{(3kN_AT)/(352 g/mol)}` ..[1]

Root mean square speed of
`^(235)UF_6=\\u '`

Molar mass of
`^(235)UF_6=M'=235 g/mol+6* 19 g/mol=349 g/mol`

`\\u '=\sqrt{(3kN_AT)/(M')}`

`\\u '=\sqrt{(3kN_AT)/(349 g/mol)}` ..[2]

[1] ÷ [2]

`(\\u )/(\\u ')=\frac{\sqrt{(3kN_AT)/(352 g/mol)}}{\sqrt{(3kN_AT)/(349 g/mol)}}`

`(\\u )/(\\u ')=\sqrt{(352 g/mol)/(349 g/mol)}=1.0042:1`

1.0042:1 is the ratio of the root mean square speed of
`^(238)UF_6` to that of
`^(235)UF_6` at constant temperature.