APPENDIX
SIMULTANEOUS DETERMINATION OF A NUMBER OF RADIOELEMENTS
If a specimen is known to contain several different radioelements, these
individual
activities may be determined simultaneously when (a) the radiation
from each radioelement can be detected and (b) the comparative efficiencies of
detection among the radioelements are different under various conditions.
is unnecessary to have a detector which
radioelements.
It
selectively detects only one of the
The specimen and a standard for each of the N radioelements
contained are each counted under N different conditions.
Let:
the fraction of radioelement (a) in the specimen
y = the fraction of radioelement (b) in the specimen
z = the fraction of radioelement (c) in the specimen
the count rate of a standard of radioelement (a)
B = the count rate of a standard of radioelement (b)
C = the count rate of a standard of radioelement (c)
K = the count rate of the specimen
In the specimen, the sum of individual count rates = the total count rate.
Ayx + By =Cyz +. . 2 = Ky
(at condition 1)
Asx + Boy + Coz tee 2 = Ky
(at condition 2)
A3x + Bay + Cz t+... = Ke
(at condition 3)
The solution to these simultaneous equations gives the fraction of the
activity of each standard which is present in the specimen.