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.
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Fig. 91.
225. Equations of rise of excited activity. The curves
expressing the gradual increase to a maximum of the excited