x] RADIO-ACTIVE PROCESSES 333 
of radium, about half a milligram disintegrates per year. Since 
the amount of radium which is unchanged will diminish according 
to an exponential law with the time, half of a given weight of 
radium will be transformed in about 1500 years. Only one per 
cent. will remain unchanged after a lapse of about 10,000 years. 
In a gram of uranium or thorium, where the change takes place 
at about one-millionth the rate, about a million years would be 
required before half a milligram would be changed. All but one 
per cent. of the uranium and thorium would be transformed in 
about 10” years. 
This is the minimum estimate of the life of radio-elements on 
the assumption that one a particle is expelled at each change. A 
maximum limit to the life of the radio-elements can be deduced 
by supposing that the radium is completely disintegrated into a 
particles. Since the mass of the a particle is about twice that of 
the hydrogen atom there cannot be many more than 100 a particles 
produced from each atom of the radio-elements. The maximum 
estimate of the life of radium is thus about 5:0 times greater 
than the minimum estimate. The minimum estimate is however 
probably nearer the truth; for there is no evidence to show that 
more than one a particle is expelled at each change. The agree- 
ment between the calculated and experimental values of the 
volume of the emanation (see section 197) is strong evidence in 
support of the minimum estimate; for in the calculation only one 
a particle was supposed to be expelled at each change. 
The changes in radium are thus fairly rapid, and a mass of 
radium if left to itself should in the course of a few thousand years 
have lost a large proportion of its radio-activity. Taking the 
minimum estimate of the life of radium, the value of X 1s 44x 1074, 
with a year as the unit of time. A mass of radium left to itself 
should thus be half transformed in 1500 years and only one- 
milhonth part would remain after 30,000 years. Thus supposing, 
for illustration, that the earth was originally composed of pure 
radium, its activity per gram 30,000 years later would not be 
greater than the activity observed to-day in a good specimen of 
pitchblende. Even taking the maximum estimate of the life of 
radium, the time required for the radium to practically disappear 
is short compared with the probable age of the earth. We are 
