I have the question:
"If a rock has a parent:daughter isotope ratio of 1:10 and the parent isotope is Rb-87, given that the half-life of Rb-87 is 48800 x 10^6 years. Calculate the age of the rock sample. "
here is my attempt is this correct ?
Parent Isotope = 1
Daughter Isotope = 10
so, Number of left parent isotope/ number of net isotope initially = 1/11
= ln(2)/48.8*10^9 [ half life of the sample]
so, t = 168.82*10^9 years
Is this correct ?
Well, the equation for $t$ is $\large{\frac{1}{11}=2^{-\frac{t}{4.88 \cdot 10^{10}}}}$ or $\large{11=2^{\frac{t}{4.88 \cdot 10^{10}}}}$. Thus, $t=\frac{\ln 11}{\ln 2} \cdot 4.88 \cdot 10^{10} \approx 1.6882 \cdot 10^{11}$