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An Introduction to Thermal Physics
Found in: Page 13
An Introduction to Thermal Physics

An Introduction to Thermal Physics

Book edition 1st
Author(s) Daniel V. Schroeder
Pages 356 pages
ISBN 9780201380279

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Short Answer

Uranium has two common isotopes, with atomic masses of 238 and 235. one way to separate these isotopes is to combine the uranium with fluorine to make uranium hexafluoride gas, UF6, then exploit the difference in the average thermal speeds of molecules containing the different isotopes. Calculate the rms speed of each molecule at room temperature, and compare them.

Speed of the lighter isotope of UF6 is more than the speed of heavier isotope of UF6

See the step by step solution

Step by Step Solution

Step 1 : Calculation of atomic mass of each isotope .

Atomic mass of UF6 is calculated as,

mUF6=mU+6mFGiven that for U238, mU=238 amu and mF=19amuThus mUF6=238+6(19)=352 amuSimilarly for U235, mU=235amu and mF=19amumUF6=235+6(19)=349 amu

Step 2 : Getting the mass in kg for each isotope 

The mass of each UF6 atom is calculated as,

m=mUF6NA where NA=6.023×1023/moleThus for U238, m=352×10-3kg/mol6.023×1023m=5.844×10-25kgAnd for U235, m1=349×10-3kg/mol6.023×1023m1=5.794×10-25kg

Step 3 : Analysis of faster isotope

The rms speed of a molecule is given by,


Where K = Boltzman constant & T is absolute temperature = 300k

Now for U238, vrms=3×1.38×10-23××3005.844×10-25vrms=145.78m/sAnd for U235, v1rms=3×1.38×10-23×3005.794×10-25v1rms=146.4m/s

Thus UF6 of U235 isotope is faster than the UF6 of U238 isotope.

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