Radioisotopes used for radiotracer labeling are present in micromasses (as low as 1 X 1016g), but they have strong radiation that can be sensitively and rapidly detected. They behave identically with the labeled material during investigation without modifying its characteristics. Radiation is detected outside the equipment or pipes, so sampling or installing instruments into the material flow can be avoided.

The basic requirement for labeling with a radiotracer is that the radiotracer always has to follow the tested material proportionally during its flow; in other words, the mass rate of the tracer has to be identical to the mass rate of the tested material in each phase of the flow.

where x, X, x" are the number of atoms of the tested material in an S, Z, Z" system, y, y, y" are the number of radioactive tracer atoms in an S, Z, Z" system, A is the type of atoms of the tested material (nonradioactive), and A* is the type of atoms of the tracer (radioactive).

While an ideal tracer for every material would be its radioactive isotope, not every element has radioactive isotopes with favorable measuring characteristics. For this reason, a generally accepted and applied method is the incorporation of the radioactive atom into the tracer molecule. However, such chemical labeling is nec­essary only if tested material goes through chemical reaction or phase modification. When studying physical behavior (e. g., flow investigations), the so-called physical labeling is acceptable where the behavior of the material is affected not by chemi­cal but by physical characteristics.

However, a tracer must follow the tested material even in the case of physical labeling (e. g., a salt as tracer dissolved in water to be followed). An extreme case for physical labeling is when a radioactive colloid is bound on the surface of grained materials. In such cases, attention must be paid to the fact that radioactive concentration of fractions will be dependent on the grain size (this is called “sur­face labeling”). Only fractions with the same grain size can be labeled homogeneously.

The relationship between activity of the labeling isotope and the measurable count rate is expressed as follows:

Zrei = 2.22 X 106 Aan (count/min) (11.4)

where /rel is the measured count rate, A is the activity of the labeling radioisotope (цО), a is the number of gamma counts per decay, and n is the total measuring efficiency (n = fєG), in which f is the self-absorption efficiency, є is the counting efficiency, and G is the space angle factor.

For tracer studies, when calculating the minimal required activity of the labeling radioisotope, dilution rate in the industrial equipment and measuring accuracy also must be taken into consideration. While the former is expressed by a simple multi­plication factor, the latter can be deducted from the expected value and standard deviation of the Poisson distribution, which is applied to radioactive decay. Based on these, 1% measuring accuracy needs 10,000 counts, 0.3% accuracy needs 100,000 counts, and 0.1% accuracy needs 1,000,000 counts to be detected (see Section 14.7.1).