Question

Only 235U can be used as fuel in a nuclear reactor, so uranium for use in the nuclear industry must be enriched in this isotope. If a sample of enriched uranium has an average atomic mass of 237.662 amu, what percentage of 235U is present?

Answer 1

While there are a number of isotopes of Uranium, for this problem assume there are only 2; i.e., U-238 and U-235 giving a weight average of 237.662 amu. Therefore, for this, %U-235 => 11.3% w/w & U-238 => 88.7% w/w.

Explanation:

The relationship for such an analysis is generally given as ...
`X_i*A_i` + `X_j*A_j` = Wt Avg Atomic Mass
`X_i + X_j` = 1.000
`X_i and X_j` => fractional abundance of each isotope
`A_i and A_j` => Atomic Mass of each isotope
Substitute isotopic mass into Wt Avg equation and solve as simultaneous equations.

`So, "for"color(white)* U-235 and U-238` ...
`X_(235)*235 + X_(238)*238 = 237.662`
`X_(235) + X_(238) = 1.000` => `X_(238) = 1.000 - X_(235)`

=> `X_(235)*235 + (1.000 - X_(235))*238 = 237.662`
=> `X_(235)*235 + 238.000 - X_235*238 = 237.662`
=> `3*X_(235) = 238.000 - 237.662 = 0.338`
=> `X_(235) = (0.338/3) = 0.113`
=> `X_(238) = 1 - 0.113 = 0.887`

In Weight Percents ...
`%U-235 = 11.3 wt%` of sample
`%U-238 = 88.7 wt%` of sample