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

Respuesta :

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.