Question

There are two important isotopes of uranium, 235U

Answer 1

Answer:

a) (vᵣₘₛ₁/vᵣₘₛ₂) = 1.00429

where vᵣₘₛ₁ represents the vᵣₘₛ for 235-UF6 and vᵣₘₛ₂ represents the vᵣₘₛ for 238-UF6.

b) T = 767.34 K

c) The answers point to a difficult seperation technique, as the two compounds of the different isotopes have very close rms speeds and to create a difference of only 1 m/s In their rms speeds would require a high temperature of up to 767.34 K.

Explanation:

The vᵣₘₛ for an atom or molecule is given by

vᵣₘₛ = √(3RT/M)

where R = molar gas constant = J/mol.K

T = absolute temperature in Kelvin

M = Molar mass of the molecules.

₁₂

Let the vᵣₘₛ of 235-UF6 be vᵣₘₛ₁

And its molar mass = M₁ = 349.0 g/mol

vᵣₘₛ₁ = √(3RT/M₁)

√(3RT) = vᵣₘₛ₁ × √M₁

For the 238-UF6

Let its vᵣₘₛ be vᵣₘₛ₂

And its molar mass = M₂ = 352.0 g/mol

√(3RT) = vᵣₘₛ₂ × √M₂

Since √(3RT) = √(3RT)

vᵣₘₛ₁ × √M₁ = vᵣₘₛ₂ × √M₂

(vᵣₘₛ₁/vᵣₘₛ₂) = (√M₂/√M₁) = [√(352)/√(349)]

(vᵣₘₛ₁/vᵣₘₛ₂) = 1.00429

b) Recall

vᵣₘₛ₁ = √(3RT/M₁)

vᵣₘₛ₂ = √(3RT/M₂)

(vᵣₘₛ₁ - vᵣₘₛ₂) = 1 m/s

[√(3RT/M₁)] - [√(3RT/M₂)] = 1

R = 8.314 J/mol.K, M₁ = 349.0 g/mol = 0.349 kg/mol, M₂ = 352.0 g/mol = 0.352 kg/mol, T = ?

√T [√(3 × 8.314/0.349) - √(3 × 8.314/0.352) = 1

√T (8.4538 - 8.4177) = 1

√T = 1/0.0361

√T = 27.7

T = 27.7²

T = 767.34 K

c) The answers point to a difficult seperation technique, as the two compounds of the different isotopes have very close rms speeds and to create a difference of only 1 m/s In their rms speeds would require a high temperature of up to 767.34 K.