Page:Radio-activity.djvu/411

 convenience collected below, where λ_{1} = 3·8 × 10^{-3}, λ_{2} = 5·38 × 10^{-4}, λ_{3} = 4·13 × 10^{-4}:—

(1) Short exposure: activity measured by β rays,

I_{t}/I_{T} = 10·3(e^{-λ_{3}t} - e^{-λ_{2}t}),

where I_{T} is the maximum value of the activity;

(2) Long exposure: activity measured by β rays,

I_{t}/I_{0} = 4·3 e^{-λ_{3}t} - 3·3 e^{-λ_{2}t},

where I_{0} is the initial value;

(3) Any time of exposure T: activity measured by the β rays,

I_{t}/I_{0} = (ae^{-λ_{3}t} - be^{-λ_{2}t})/(a - b),

where

a = (1 - e^{-λ_{3}T})/λ_{3}, b = (1 - e^{-λ_{2}T})/λ_{2};

(4) Activity measured by α rays: long time of exposure,

I_{t}/I_{0} = (1/2)e^{-λ_{1}t} + (1/2)(4·3 e^{-λ_{3}t} - 3·3 e^{-λ_{2}t}).

The equations for the α rays for any time of exposure can be readily deduced, but the expressions are somewhat complicated.

Fig. 91.

225. Equations of rise of excited activity. The curves expressing the gradual increase to a maximum of the excited