. Radio-activity . yS, and y rays; (4) A fourth very slow change will be discussed later. 224. Equations representing the activity curves. The equations representing the variation of activity with time are for XI] TEANSFOEMATION PEODUCTS OF EADIUM 389 convenience collected below, where Xi = 38 x 10 ^ \2 = 538 x 10 *,Xs = 4-13 X 10-* :— (1) Short exposure: activity measured by /3 rays, 7J/r=10-3(e-V-e-^^0>where Irp is the maximum value of the activity; (2) Long exposure : activity measured by /3 rays, /^//o = 4-3e-^3i-3-3e-^^^where Iq is the initial value; (3) Any time of exposure T: activit
. Radio-activity . yS, and y rays; (4) A fourth very slow change will be discussed later. 224. Equations representing the activity curves. The equations representing the variation of activity with time are for XI] TEANSFOEMATION PEODUCTS OF EADIUM 389 convenience collected below, where Xi = 38 x 10 ^ \2 = 538 x 10 *,Xs = 4-13 X 10-* :— (1) Short exposure: activity measured by /3 rays, 7J/r=10-3(e-V-e-^^0>where Irp is the maximum value of the activity; (2) Long exposure : activity measured by /3 rays, /^//o = 4-3e-^3i-3-3e-^^^where Iq is the initial value; (3) Any time of exposure T: activity measured by the /3 rays, where L 1 - e^^T 1 a = :: , 0 = — ^ X3 A-a (4) Activity measured by a rays : long time of exposure. = 1 e-^^* + 1 (4-3 e-^3* _ 3-3 g-M). The equations for the a rays for any time of exposure can bereadily deduced, but the expressions are somewhat complicated. 225. Equations of rise of excited activity. The curves expressing the gradual increase to a maximum of the excited ioo„. 30 40 Time in Minutes. Fig. 91. 390 TRANSFORMATION PRODUCTS OF RADIUM [CH. activity produced on a body exposed in the presence of a constantamount of emanation are complementary to the curves of decay fora long exposure. The sum of the ordinates of the rise and decaycurves is at any time a constant. This follows necessarily from thetheory and can also be deduced simply from a priori considerations.(See section 200.) The curves of rise and decay of the excited activity for boththe a and /8 rays are shown graphically in Fig. 91. The thick linecurves are for the a rays. The difference between the shapesof the decay curves when measured by the u or /3 rays is clearlybrought out in the figure. The equations representing the rise ofactivity to a maximum are given below. For the /3 and <y rays, It/Ima. = 1 - (4-3 6-^3^ - 3-3 e-^t).For the a rays, /^//max = 1 - i e-^i - 1 (4-3 e-^i - 3-3 e-^^0- 226. Effect of temperature. We have so far not con-sidered the evidence on whi
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