Chemistry Reference
In-Depth Information
Unst
able parent nucleu
s
α
,
β
−
,β
+
,E.C.,
γ
,
Excited state
Excited state
α
,d,p,n,
γ,..
γ
e
-
,
X
γ
C.E
.
Stable nucleus
Ground state
Ground state
Detector
Doppler velocity
Fig. 1.1
Schematic illustration of the source and the absorber in a Mössbauer experiment
Finally this excited states decay to ground state of the Mössbauer nucleus. For
57
Fe,
57
Co decays to two excited states of
57
Fe, but decays 99.8 % to the lowest
energy level 14.4 keV that is called as a first excited state from ground state of
57
Fe. Ground state of
57
Fe is a stable nucleus and shows no decay. Each nuclear
level has a unique energy, spin, parity and decay constant k (probability of
decaying per unit time). Ground state is, of course, zero energy and decay constant
is zero.
1.1.2 Decay
1
From the definition of k, the number decay in a time dt is given by
dN
¼
kN
ð
t
Þ
dt
ð
1
:
1
Þ
where N
ð
t
Þ
is the number of particles present at time t. Integration yields the
exponential decay law,
N
ð
t
Þ¼
N
ð
0
Þ
e
kt
:
ð
1
:
2
Þ
Figure
1.2
shows log N
ð
t
Þ
versus t. Half-life and mean life (lifetime) are indi-
cated. The mean life is the average time a particle exists before it decays; it is
connected to k and t
1
=
2
by
s
¼
1
k
¼
t
1
=
2
ln 2
¼
1
:
44t
1
=
2
:
ð
1
:
3
Þ
1
Frauenfelder H. and. Henly M. E: Subatomic Physics (Prentice-Hall, Inc., Englewood Cliffs,
New Jersey 1974).
