There are two important isotopes of uranium -^235U and ^238U; these isotopes are

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 speeds v_rms of uranium hexafluoride gas, UF_6. (Use k = 1.38 Times 10^-23 J/K for this question.) The molecular masses for ^235UF_6 and ^238UF_6 are 349.0 g/mol and 352.0 g/mol, respectively. What is the ratio of their average speeds? (Enter your answer to at least 4 decimal places.) Use the kinetic theory of gases to find the ratio of the rms velocities. At what temperature would their average speeds differ by 1.20 m/s?

Explanation / Answer

a)

Let, M_235 = 349 g/mol = 0.349 kg/mol

M_238 = 353 g/mol = 0.353 kg/mol

we know, Vrms = sqrt(8*R*T/(pi*M))

so, V_235/V_238 = sqrt(M_238/M_235)

= sqrt(353/349)

= 1.00571 <<<<<<<------------Answer

b)

Let T is the required temperature.

V_235 - V_238 = sqrt(8*R*T/(pi*M_235)) - sqrt(8*R*T/(pi*M_238))

1.2 = sqrt(8*8.314*T/(pi*0.349)) - sqrt(8*8.314*T/(pi*0.353))

= 7.78865*sqrt(T) - 7.7444*sqrt(T)

= 0.04425*sqrt(T)

sqrt(T) = 1.2/0.04425

T = (1.2/0.04425)^2

= 735.4 K <<<<<<<------------Answer

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