
35Physical Basis of Nuclear Forensic Science
Only total decay constants should be used in the equations that follow. Consider
t
he
ca
se
i
n
w
hich
A
d
ecays to
B
,
w
hich
i
n
t
urn
d
ecays
w
ith
a
d
ecay
c
onstant
λ
B
. If a
d
ecay equation analogous to Equation 2.1 is constructed,
− = −d d
B B B A A
N t N Nλ λ . (2.3)
As
b
efore,
t
he
r
ate
o
f
d
ecay
o
f
B
i
s
p
roportional
t
o
t
he
n
umber
o
f
at
oms
o
f
B
,
N
B
. In
t
his
ca
se,
t
he
r
ate
o
f
i
ngrowth
o
f
B
i
s
e
qual
t
o
t
he
i
nstantaneous
r
ate
at
w
hich
A
i
s
d
ecaying,
λ
A
N
A
. If Equation 2.2 is substituted into Equation 2.3 to eliminate N
A
, and
t
he differential equation is solved,
N N t t t t
N
B A A B A A B
B
= −
( )
− − − −
{ }
+
λ