• :00Days
• :00Hours
• :00Mins
• 00Seconds
A new era for learning is coming soon Suggested languages for you:

Europe

Answers without the blur. Sign up and see all textbooks for free! 1.2.

Expert-verified Found in: Page 13 ### An Introduction to Thermal Physics

Book edition 1st
Author(s) Daniel V. Schroeder
Pages 356 pages
ISBN 9780201380279 # 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 1 : Calculation of atomic mass of each isotope .

Atomic mass of UF6 is calculated as,

${m}_{U{F}_{6}}={m}_{U}+6mF\phantom{\rule{0ex}{0ex}}Giventhatfor{U}^{238},{m}_{U}=238amuand{m}_{F}=19amu\phantom{\rule{0ex}{0ex}}Thus{m}_{U{F}_{6}}=238+6\left(19\right)=352amu\phantom{\rule{0ex}{0ex}}Similarlyfor{U}^{235},{m}_{U}=235amuand{m}_{F}=19amu\phantom{\rule{0ex}{0ex}}{m}_{U{F}_{6}}=235+6\left(19\right)=349amu$

## Step 2 : Getting the mass in kg for each isotope

The mass of each UF6 atom is calculated as,

$m=\frac{{m}_{U{F}_{6}}}{{N}_{A}}where{N}_{A}=6.023×{10}^{23}/mole\phantom{\rule{0ex}{0ex}}Thusfor{U}^{238},m=\frac{352×{10}^{-3}kg/mol}{6.023×{10}^{23}}\phantom{\rule{0ex}{0ex}}m=5.844×{10}^{-25}kg\phantom{\rule{0ex}{0ex}}Andfor{U}^{235},{m}^{1}=\frac{349×{10}^{-3}kg/mol}{6.023×{10}^{23}}\phantom{\rule{0ex}{0ex}}{m}^{1}=5.794×{10}^{-25}kg$

## Step 3 : Analysis of faster isotope

The rms speed of a molecule is given by,

vrms=$\sqrt{\frac{3KT}{m}}$

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

Now for ${U}^{238},{v}_{rms}=\sqrt{\frac{3×1.38×{10}^{-23}××300}{5.844×{10}^{-25}}}\phantom{\rule{0ex}{0ex}}{v}_{rms}=145.78m/s\phantom{\rule{0ex}{0ex}}Andfor{U}^{235},{{v}^{1}}_{rms}=\sqrt{\frac{3×1.38×{10}^{-23}×300}{5.794×{10}^{-25}}}\phantom{\rule{0ex}{0ex}}{{v}^{1}}_{rms}=146.4m/s\phantom{\rule{0ex}{0ex}}$

Thus UF6 of U235 isotope is faster than the UF6 of U238 isotope. ### Want to see more solutions like these? 