The solution of this equation is of the form
Q = n(ae^{-λ_{1}t} + be^{-λ_{2}t}) (3).
By substitution it is found that a = λ_{1}/(λ_{2} - λ_{1}).
Since Q = 0 when t = 0, b = -λ_{1}(λ_{2} - λ_{1}).
Thus Q = (nλ_{1}/(λ_{1} - λ_{2}))(e^{-λ_{2}t} - e^{-λ_{1}t}) (4).
Substituting this value of Q in (2), it can readily be shown that
R = n(ae^{-λ_{1}t} + be^{-λ_{2}t} + ce^{-λ_{3}t}) (5),
where
a = λ_{1}λ_{2}/((λ_{1} - λ_{2})(λ_{1} - λ_{3})), b = -λ_{1}λ_{2}/((λ_{1} - λ_{2})(λ_{2} - λ_{3})),
c = λ_{1}λ_{2}/((λ_{1} - λ_{3})(λ_{2} - λ_{3})).
 | An image should appear at this position in the text. To use the entire page scan as a placeholder, edit this page and replace "{{missing image}}" with "{{raw image|Radio-activity.djvu/354}}". Otherwise, if you are able to provide the image then please do so. For guidance, see Wikisource:Image guidelines and Help:Adding images. |  |
Relative number of atoms of matter A.B.C. present at any time (Case 1).
Fig. 72.
The variation of the values of P, Q, R with the time t, after removal of the source, is shown graphically in Fig. 72, curves A, B, and C respectively. In order to draw the curves for the practical case which will be considered later corresponding to the first three
