Half lives of two isotopes X and Y of a material are known to be $2\times {10}^9$ years and $4\times {10}^9$ years respectively. If a planet was formed with equal number of these isotopes, then the current age of planet, given that currently the material has 20 % of X and 80% of Y by number, will be

Q.

Half lives of two isotopes X and Y of a material are known to be $2\times {10}^9$ years and $4\times {10}^9$ years respectively. If a planet forms with equal number of these isotopes , estimate the current age of the planet, given that currently the material has 20% of X and 80% of Y by number

Q. A radio isotope X with a half life $1.4\times {10}^9$ years decays to Y, which is stable. A sample of the rock from a cave was found to contain X and Y in the ratio 1 : 7. The age of the rock is

Q. The present day abundances of the isotopes ${\bigcup }^{238}$ and ${\bigcup }^{235}$ are in the ratio of $128:1$. They have half lives of $4.5\times {10}^9$ years and $7\times {10}^8$ years respectively and assume that the equal amount of each isotope existed at the time of formation of the earth. If age of earth is $\frac{49X}{76}\times {10}^9$ years, then calculate X

Q.

At radioactive equilibrium, the ratio between the number of the atoms of two radioactive elements (X) and (Y) was found to be $3.2\times {10}^9$ : 1 respectively. If half-life of the element (X) is $1.6\times {10}^{10}$ years, then half-life of the element (Y) would be

Q. In a chemical analysis of a rock, the mass ratio of two radioactive isotopes is found to be $100:1$. The mean lives of the two isotopes are $4\times {10}^9\text{years}$ and $2\times {10}^9\text{years}$, respectively. If it is assumed that at the time of formation, atoms of both the isotopes were in equal proportion, calculate the age of rock. Ratio of the atomic weight of the two isotopes is $1.02:1$.
Given ${\log }_e\left(100/1.02\right)=4.58$