For the sake of illustration, we shall consider the variation of the activity of the active deposit of thorium, due to a very short exposure to the emanation. Thorium A gives out no rays, and thorium B gives out α, β, and γ rays, while thorium C is inactive.
The matter A is half transformed in 11 hours, and B is half transformed in 55 minutes. The value of λ1 = 1·75 x 10-5(sec.)-1 and λ2 = 2·08 x 10-4(sec.)-1.
The activity of the mixture of products A + B is due to B alone, and will, in consequence, be always proportional to the amount of B present, that is, to the value of Q.
The variation of activity with time is shown graphically in Fig. 76. The activity rises from zero to a maximum in 220 minutes and then decays, finally decreasing, according to an exponential law, with the time, falling to half value in 11 hours.
This theoretical curve is seen to agree closely in shape with the experimental curve (Fig. 65), which shows the variation of the activity of the active deposit of thorium, produced by a short exposure in presence of the emanation.
There are several points of interest in connection with an activity curve of this character. The activity, some hours after removal, decays according to an exponential law, not at the rate of the product B , from which the