244
11. .SPONTANEOUS _DlSINTEGRATION
different beta ray electroscopes. Their activity curves are shown “
-
in gure 11—3.
Curve  shows the beta ray activity in the '
uranium I sample and hence shows the formation of uranium Xl
,
(since uranium I does not emit beta rays). Curve B shows the
decay of the isolated uranium X1.
In order to show that this is
_
the decay curve of uranium Xl and not of its disintegratiQ,n
products, the following series is given.
,
a
B, 7
B, 7
a
‘
UI /———> UX1 /——> UX2 /——> un L
_
-
4.4 X 109 years
24.5 days
1.14 minutes
3 X 105 years
‘
The gures which are given are thetimes for half of the substance
_
to decay. It is to be noted that neither uranium l or H contribute
_
to the activity as they emit only alpha particles and a beta ray
electroscope is used. The beta rays of uranium X2 constitute
_
the major activity of the curve 8 of gure
but, since this «
substance decays quickly, it is its continual replenishment by
uranium Xl which determines the shape of the Curve, ie, the
«_
shape of B is determined by uranium Xl, although it is actually
;
due to uranium X2.
The fact that a decay curve follows the
_
activity of a long—life substance in spite of the presence
of its short—
-
lived products is a general principle in this subject.
'
'
11+6.
Rutheord—Soddy Theory of Transformations. IsôSubstances._—lt is assumed that the number of atoms which
break up each second is
constant fraction of those present at
any given instant._ For example, if there are 10,000 atomsat
thestart and 200 (2%) break up during the rst second, send1ng
out an alpha or beta and gamma ray, then during the next second
2per
cent (196) of the remaining 9800 atoms
break up and
during the third second 2 per cent of the remaining atoms break
_
_
up,
theÿôO4 will disintegrate, etc. The ratio. ofthe
number which break up each second to the total number is called
thetmmformaz‘zon or disinægmz‘ian constant and is desgnatedby>x
'
WhereN is thetotal number present at a Certain time
number Whlchbreak up”-at that timeduriñg
We\then
have
‘
“:
_
J
:
…
«]
"
,
5
_
Æ__
) :
_
11. .SPONTANEOUS _DlSINTEGRATION
different beta ray electroscopes. Their activity curves are shown “
-
in gure 11—3.
Curve  shows the beta ray activity in the '
uranium I sample and hence shows the formation of uranium Xl
,
(since uranium I does not emit beta rays). Curve B shows the
decay of the isolated uranium X1.
In order to show that this is
_
the decay curve of uranium Xl and not of its disintegratiQ,n
products, the following series is given.
,
a
B, 7
B, 7
a
‘
UI /———> UX1 /——> UX2 /——> un L
_
-
4.4 X 109 years
24.5 days
1.14 minutes
3 X 105 years
‘
The gures which are given are thetimes for half of the substance
_
to decay. It is to be noted that neither uranium l or H contribute
_
to the activity as they emit only alpha particles and a beta ray
electroscope is used. The beta rays of uranium X2 constitute
_
the major activity of the curve 8 of gure
but, since this «
substance decays quickly, it is its continual replenishment by
uranium Xl which determines the shape of the Curve, ie, the
«_
shape of B is determined by uranium Xl, although it is actually
;
due to uranium X2.
The fact that a decay curve follows the
_
activity of a long—life substance in spite of the presence
of its short—
-
lived products is a general principle in this subject.
'
'
11+6.
Rutheord—Soddy Theory of Transformations. IsôSubstances._—lt is assumed that the number of atoms which
break up each second is
constant fraction of those present at
any given instant._ For example, if there are 10,000 atomsat
thestart and 200 (2%) break up during the rst second, send1ng
out an alpha or beta and gamma ray, then during the next second
2per
cent (196) of the remaining 9800 atoms
break up and
during the third second 2 per cent of the remaining atoms break
_
_
up,
theÿôO4 will disintegrate, etc. The ratio. ofthe
number which break up each second to the total number is called
thetmmformaz‘zon or disinægmz‘ian constant and is desgnatedby>x
'
WhereN is thetotal number present at a Certain time
number Whlchbreak up”-at that timeduriñg
We\then
have
‘
“:
_
J
:
…
«]
"
,
5
_
Æ__
) :
_