Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
Home  >>  JEEMAIN and AIPMT  >>  Physics  >>  Class12  >>  Atoms
0 votes

In chain analysis of a rock , the mass ratio of two radioactive isotope is found to be $\;100 \%\;$ . The mean lives of two isotopes are $\;4 \times 10^{9}\;$years and $\;2\times10^{9}\;$years respectively . If it is assumed that at time of formation of rock , both isotopes were in equal proportion . Then calculate age of rock . Ratio of atomic weights of two isotope is $\;1.02 \%\;(log_{10}^{1.02}=0.0086)$

$(a)\;18.3 \times 10^{9} \;years\qquad(b)\;19.2 \times 10^{10} \;years\qquad(c)\;20.2 \times 10^{11} \;years\qquad(d)\;11.6 \times 10^{8} \;years$

Can you answer this question?

1 Answer

0 votes
Answer : $\;18.3 \times 10^{9} \;years$
Explanation :
At time of formation of rock , both isotopes have same no.of nuclei No. Let $\;\lambda_{1}\;$ & $\;\lambda_{2}\;$ be decay constants of two isotopes .
If $\;N_{1}\;$ and $\;N_{2}\;$ are no.of their Nuclei after a time t , we have
$N_{1}=N_{0} e^{-\lambda_{1} t }\;$ & $\;N_{2}=N_{0} e^{-\lambda_{2} t}\;$
Let mass of two isotopes at time t be $\;m_{1}\;$ & $\;m_{2}\;$ and let their respective atomic weights be $\;M_{1}\;$ and $\;M_{2}\; $ we have
$m_{1}=N_{1} M_{1}\;$ & $\;m_{2}=N_{2} M_{2}$
Substituting value given in problem we get
Let $\;z_{1}\;$ & $\;z_{2}\;$ be mean lives of two isotopes .Then
$z_{1}=\large\frac{1}{\lambda_{1}}\;$ and $\;z_{2}=\large\frac{1}{\lambda_{2}}$
Which gives
$\;\lambda_{1}-\lambda_{2}=\large\frac{z_{1}-z_{2}}{z_{1} z_{2}}=\large\frac{2 \times10^{9}-4\times10^{9}}{2 \times10^{9}\times4\times10^{9}}$$=-0.25\times10^{-9}$
Setting this value in equation (1) we get
or $\;t=\large\frac{1}{0.25\times10^{-9}}\;log_{e} \large\frac{(100)}{1.02}$$=18.34 \times 10^{9} year\;.$
answered Feb 27, 2014 by yamini.v
edited Mar 26, 2014 by balaji.thirumalai

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, AIPMT Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App