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Q.46

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 568

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Short Answer

Uranium has two naturally occurring isotopes. has a natural abundance of and has an abundance of . It is the rarer that is needed for nuclear reactors. The isotopes are separated by forming uranium hexafluoride, , which is a gas, then allowing it to diffuse through a series of porous membranes. has a slightly larger rms speed than and diffuses slightly faster. Many repetitions of this procedure gradually separate the two isotopes. What is the ratio of the rms speed of to that of

Root mean square velocity of is.

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Step by Step Solution

Step 1: Formula for average translational kinetic energy  

The average translational kinetic energy is

The molecule with massand velocity has an average translational kinetic energy,

Step 2: Calculation for root mean square velocity

Equating equationandhave the same left side,

Root mean square velocity is,

The root square of the molar mass is inversely proportional to root mean square velocity.

The molar mass of fluorineis.

So, the molar mass of is,is.

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