246
11.
SPONTANEOUS DISINTEGRATION
for curve B of gure 11—3 in a different manner.
If the ordinates
are logE ] and the abscissae the time, a straight curve will result
whose negative slope is >\, the transformation constant.
The mean or average lzfe (L) of a radioactive substance is given
by the relation,*
;
'
‘
1
L —
(11 11)
Substituting this time for i in the transformation law gives N /No
=
1/_e.
In other words, during the average life of a substance
1/2.718+ of it will disintegrate.
-
_
The third constant is the one most widely used and is called
the half life period or half life (T) It is the number of seconds for
'
the activity to fall to half its original value, i.e., for half the atoms
to break up. Then N/No = % = €“; — logE 2 = —
whence
.
T =
91î—9Ë
=
0.693L.
(11—12)‘
As an example, the transformation constant >\ of radium is
1.35 X
seconds—1. This means that approximately one atom
in every 1011 atoms breaks up each second.
From equation 11—12,
the half period T is equal to 1590 years. If one had a gram of .
radium today, he would_have only one-half a gram at the end of
1590 years, one—quarter of a gram at the end of 3180 years, one—
eighth of a gram at the end of the next 1590 years, etc.
'
._
The radioactive constants are characteristic of a given sub—
_
stance and allow its identication equally as well as chemical
analysis. They may be measured directly if the substance can be
isolatedfrom its parent and products _or they may be deduced from
'
the activity curves.
The constants may also be
_measuremwtsçh the range of alpha particles together Withthe
relation discussed inthe next chapter
are not of high accuracy.
"
_
,'
Ï
'
is obtained if the number Of
«
observed Wltha
:= ‘
uorescentscreen or Géiger counter, is dividedby the number0{
î. :
atoms per grar
of the” “substance. ; The number of. atoms êpèngram
L==1/À
“