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?

1 Answer
Mar 29, 2018

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