# Effusion and isotopic composition

• Pouyan
In summary, in the process of enriching the fissile isotope 235U, a gas UF6 with natural isotopic composition is allowed to undergo an effusion process. This process is repeated multiple times to progressively increase the concentration of 235U. The value of n, when the concentration increases from 0.7% to 0.8%, is approximately 33.5. The formula used for this calculation takes into account the number of collisions between molecules of different masses, with pressure and temperature assumed to be constant.
Pouyan
1. In a gas UF6 (uranium hexafluoride) are uranium atoms of both the fissionable uranium isotope 235U , and 238U. To enrich the fissile isotope can let a gas UF6 with natural isotopic composition (0.7% 235U, 99.3% 238U) undergo effusion process. The process is then repeated in many steps in the effusion process, so that 235U progressively enriched, from the initial concentration of 0.7%. After enrichment in the first step of the process, the concentration of 235U increased from 0.7% to k * 0.7%. After the enrichment step n is the concentration (k^n) * 0.7%. What is the value of n when the concentration increased to 0.8% ?! we assume that the system is built so that molecules can not pass back to the original volume of gas, once again gone through the small holes (channels) that give rise to effusion. Relative atomic mass of fluorine is 19

## Homework Equations

I know the formula :

v*= p/(sqrt(2pi*m*k*T))

p= pressrue
k= Boltzman constant
m= mass
T = temperature

## The Attempt at a Solution

I know k is the number of collision for (235)UF6 and (238)UF6. In this case :

v* for (235)UF6 / v* (238)UF6
which will be
k= sqrt(m for (238)UF6 / m for (235)UF6) = sqrt((238 + 6*19)/235+6*19) = 1.004

and (1.004) ^n = 0.8/0.7

n= 33.5

This is my attempt and the original answer is a number near to it. My question is :

Should I think that pressure and temperature are constants in this case and the only variable is m ?!

Can somebody help me ?!

Last edited:

## 1. What is effusion?

Effusion refers to the process by which a gas escapes through a small opening into a vacuum. It is also known as the diffusion of gases through an orifice.

## 2. How does effusion occur?

Effusion occurs due to the difference in pressure between the two sides of the opening. The gas molecules on the high-pressure side collide with each other and escape through the opening, while the gas molecules on the low-pressure side do not have enough collisions to escape.

## 3. What is the significance of isotopic composition in effusion?

The isotopic composition of a gas refers to the relative abundance of different isotopes (atoms with the same number of protons but different number of neutrons) in the gas. This composition can affect the rate of effusion, as lighter isotopes tend to effuse more quickly than heavier ones.

## 4. How is the isotopic composition of a gas measured?

The isotopic composition of a gas can be measured using techniques such as mass spectrometry, which separates and analyzes the different isotopes present in a sample of gas.

## 5. What are some potential applications of studying effusion and isotopic composition?

Effusion and isotopic composition have various applications in fields such as atmospheric science, geochemistry, and nuclear physics. They can provide insights into the origins and evolution of different gases and help in understanding processes such as diffusion and chemical reactions in different environments.

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