Answer:
1.0042:1 is the ratio of the root mean square speed of [tex]^{238}UF_6[/tex] to that of [tex]^{235}UF_6[/tex] at constant temperature.
Explanation:
The formula used for root mean square speed is:
[tex]\nu_{rms}=\sqrt{\frac{3kN_AT}{M}}[/tex]
where,
[tex]\nu_{rms}[/tex] = root mean square speed
k = Boltzmann’s constant = [tex]1.38\times 10^{-23}J/K[/tex]
T = temperature = 370 K
M = atomic mass = 0.02 kg/mole
[tex]N_A[/tex] = Avogadro’s number = [tex]6.02\times 10^{23}mol^{-1}[/tex]
Root mean square speed of [tex]^{238}UF_6=\nu [/tex]
Molar mass of [tex]^{238}UF_6=M=238 g/mol+6\times 19 g/mol=352 g/mol[/tex]
[tex]\nu =\sqrt{\frac{3kN_AT}{M}}[/tex]
[tex]\nu =\sqrt{\frac{3kN_AT}{352 g/mol}}[/tex] ..[1]
Root mean square speed of [tex]^{235}UF_6=\nu '[/tex]
Molar mass of [tex]^{235}UF_6=M'=235 g/mol+6\times 19 g/mol=349 g/mol[/tex]
[tex]\nu '=\sqrt{\frac{3kN_AT}{M'}}[/tex]
[tex]\nu '=\sqrt{\frac{3kN_AT}{349 g/mol}}[/tex] ..[2]
[1] ÷ [2]
[tex]\frac{\nu }{\nu '}=\frac{\sqrt{\frac{3kN_AT}{352 g/mol}}}{\sqrt{\frac{3kN_AT}{349 g/mol}}}[/tex]
[tex]\frac{\nu }{\nu '}=\sqrt{\frac{352 g/mol}{349 g/mol}}=1.0042:1[/tex]
1.0042:1 is the ratio of the root mean square speed of [tex]^{238}UF_6[/tex] to that of [tex]^{235}UF_6[/tex] at constant temperature.