Question

There are two important isotopes of uranium, 235U and 238U; these isotopes are nearly identical chemically but have different atomic masses. Only 235U is very useful in nuclear reactors. Separating the isotopes is called uranium enrichment (and is often in the news as of this writing because of concerns that some countries are enriching uranium with the goal of making nuclear weapons.) One of the techniques for enrichment, gas diffusion, is based on the different molecular speeds of uranium hexafluoride gas, UF6.

(a) The molar masses of 235U and 238UF6 are 349.0 g/mol and 352.0 g/mol, respectively. What is the ratio of their typical speeds vrms?

a) 1.00
b) 0.995
c) 1.01
d) 0.985

Answer 1

The ratio of the typical root-mean-square speeds (v_rms) of 235U UF6 and 238U UF6 is approximately 0.995, determined by the inverse square root of their molar masses.

Step-by-step explanation:

To find the ratio of the typical speeds (vrms) of 235U UF6 and 238U UF6, we use the root-mean-square speed formula for gases: vrms = √(3RT/M), where R is the ideal gas constant, T is the temperature, and M is the molar mass of the gas. The ratio of the typical root-mean-square speeds (v_rms) of 235U UF6 and 238U UF6 is approximately 0.995, determined by the inverse square root of their molar masses.

Since R and T are constants for both isotopes under the same conditions, the ratio of their speeds depends only on the inverse square root of their molar masses.

The molar masses are 349.0 g/mol for 235U UF6 and 352.0 g/mol for 238U UF6. The ratio of their speeds is therefore vrms(235U UF6) / vrms(238U UF6) = √(352/349). When calculated, this ratio is approximately 0.995.