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, UF_6, 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

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1 : Calculation of atomic mass of each isotope .

Atomic mass of UF₆ is calculated as,

$m_{U F_{6}} = m_{U} + 6 m F G i v e n t h a t f o r U^{238}, m_{U} = 238 a m u a n d m_{F} = 19 a m u T h u s m_{U F_{6}} = 238 + 6 (19) = 352 a m u S i m i l a r l y f o r U^{235}, m_{U} = 235 a m u a n d m_{F} = 19 a m u m_{U F_{6}} = 235 + 6 (19) = 349 a m u$

Step 2 : Getting the mass in kg for each isotope

The mass of each UF₆ atom is calculated as,

$m = \frac{m_{U F_{6}}}{N_{A}} w h e r e N_{A} = 6.023 \times 10^{23} / m o l e T h u s f o r U^{238}, m = \frac{352 \times 10^{- 3} k g / m o l}{6.023 \times 10^{23}} m = 5.844 \times 10^{- 25} k g A n d f o r U^{235}, m^{1} = \frac{349 \times 10^{- 3} k g / m o l}{6.023 \times 10^{23}} m^{1} = 5.794 \times 10^{- 25} k g$

Step 3 : Analysis of faster isotope

The rms speed of a molecule is given by,

v_rms= $\sqrt{\frac{3 K T}{m}}$

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

Now for $U^{238}, v_{r m s} = \sqrt{\frac{3 \times 1.38 \times 10^{- 23} \times \times 300}{5.844 \times 10^{- 25}}} v_{r m s} = 145.78 m / s A n d f o r U^{235}, {v^{1}}_{r m s} = \sqrt{\frac{3 \times 1.38 \times 10^{- 23} \times 300}{5.794 \times 10^{- 25}}} {v^{1}}_{r m s} = 146.4 m / s$

Thus UF₆of U²³⁵ isotope is faster than the UF₆ of U²³⁸ isotope.

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Step by Step Solution

Step 1 : Calculation of atomic mass of each isotope .

Step 2 : Getting the mass in kg for each isotope

Step 3 : Analysis of faster isotope

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