39) In a rock sample the values of
(\frac{87_{sr}}{86_{sr}})_{parent} and (\frac{87_{Rb}}{86_{sr}})_{parent}
are 0.7125 and 0.2 respectively. The decay constant (ʎ) 87_{Rb} is 1.42 * 10-11 year -1 and
the time before present (t) is 1000 million years. The value of the initial
ratio of (\frac{87_{sr}}{86_{sr}})_{o} is ______
(Thanks to
Chandrasekhar, ANU)
Soltuion:
Given that of
(\frac{87_{sr}}{86_{sr}})_{parent} = 0.7125
(\frac{87_{Rb}}{86_{sr}})_{parent}=0.2
ʎ = 1.42 * 10-11 year -1
t = 1000 million years
= 1000*106 years =
109 years
We
know that decay equation of Rb -Sr is
(\frac{87_{sr}}{86_{sr}})_{parent}=(\frac{87_{sr}}{86_{sr}})_{o}+(\frac{87_{Rb}}{86_{sr}})_{parent}(e^{\lambda
t}-1)---------------------------(1)
By
substituting the given values in the above equation
(\frac{87_{sr}}{86_{sr}})_{parent}=(\frac{87_{sr}}{86_{sr}})_{o}+(\frac{87_{Rb}}{86_{sr}})_{parent}(e^{\lambda
t}-1)
0.7125=(\frac{87_{sr}}{86_{sr}})_{o}+0.2(e^{1.42\times
10^{-11}\times 10^{9} }-1)
0.7125=(\frac{87_{sr}}{86_{sr}})_{o}+0.2(e^{1.42\times
10^{-2} }-1)
0.7125=(\frac{87_{sr}}{86_{sr}})_{o}+0.2(e^{0.0142}-1)
0.7125=(\frac{87_{sr}}{86_{sr}})_{o}+0.2(1.0143-1)
0.7125=(\frac{87_{sr}}{86_{sr}})_{o}+0.2(0.0143)
0.7125=(\frac{87_{sr}}{86_{sr}})_{o}+0.00286
(\frac{87_{sr}}{86_{sr}})_{o}=0.7125-0.00286
(\frac{87_{sr}}{86_{sr}})_{o}=0.7096
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