Uranium-235 can be separated from U -238 by fluorinating the uranium to form UF 6 which is a gas) and then taking advantage of the different rates of effusion and diffusion for compounds containing the two isotopes.
Calculate the ratio of effusion rates for 238 UF 6 and 235 UF 6. The atomic mass of U-235 is 235.054 amu and that of U-238 is 238.051 amu.
r1 = rate for U235
r2 = rate for U238
M1 = mass U235 = 235
M2 = mass U238 = 238
(r1/r2) = sqrt(M2/M1)
To calculate the ratio of effusion rates for 238UF6 and 235UF6, we need to consider the molar mass of each compound as well as the molar mass of the individual isotopes.
The molar mass of a compound is the sum of the atomic masses of all the elements in the compound. In this case, UF6 consists of uranium (U) and six fluorine atoms (F).
First, let's calculate the molar mass of UF6:
- Uranium (U) has a molar mass of 238.051 amu (given).
- Fluorine (F) has a molar mass of 18.9984 amu (standard atomic weight).
- Since there are six fluorine atoms in UF6, the total molar mass of fluorine is 6 * 18.9984 amu.
Adding the molar masses of uranium and fluorine, we get:
Molar mass of UF6 = (1 * 238.051 amu) + (6 * 18.9984 amu).
Now, let's calculate the molar mass of 238UF6:
This is the same as the molar mass of UF6, as both contain U-238 isotopes.
Next, let's calculate the molar mass of 235UF6:
- Uranium-235 (U-235) has a molar mass of 235.054 amu (given).
- Since the compound contains U-235, the total molar mass of uranium-235 is 1 * 235.054 amu.
Now that we have the molar masses of 238UF6 and 235UF6, we can calculate the ratio of their effusion rates.
The effusion rate is inversely proportional to the square root of the molar mass. So, the ratio of effusion rates can be calculated as the square root of the ratio of molar masses.
Ratio of effusion rates = √(molar mass of 235UF6 / molar mass of 238UF6).
Substituting the calculated molar masses, the ratio of effusion rates is:
Ratio of effusion rates = √(235.054 amu / 238.051 amu).
Calculating this ratio will give you the final answer.