DECAY CONSTANT 



59 



TABLE II-l 



Substance 



Decay Constant 

 X per sec 



Half-Value 

 Period or 

 Half-Life 



Amount in Milli- 

 grams in Equilib- 

 rium with 1 Gram 

 of Radium 



The decay constant (X) for radium is 1.38 X 10 _u per sec. This 

 means that, in a group of 10 11 atoms, 1.38 on the average disintegrate 

 per second. One gram of radium contains 6.07 X 10 23 /226, or 26.8 X 10 20 

 atoms. Then 26.8 X 10 20 X 1.38 X KT 11 or 3.7 X 10 10 atoms in each 

 gram of radium disintegrate per second. 



The decay constant for radon is 2.097 X 10 -6 per sec, which means 

 that approximately 2 atoms in every million disintegrate per second. 

 In 1 gram of radon gas, 570,000 X 10 10 atoms disintegrate per second, 

 a rate which indicates that radon is more than 150,000 times as active 

 as an equal mass of radium. 



Suppose that we have 1000 relative units of radon and 1 hour later 

 we wish to use this material; how many units will still be available? 

 The following formula can be used to calculate N, the number of units 

 available after 1 hour for which t = 3600 sec. 



N = N e- Xt 



N = 1000e _2097xl0_ x3600 



loge (l55>. 



log 



in 



)- 



\1000/ 



-75.06 X 10 -4 

 75.06 X 10" 4 



2.3026 



= -32.5 X 10 



,-4 



N = 993 



