A radioactive sample decays $\frac{7}{4}$ times its original quantity in $15$ minutes. The half-life of the sample is $......min$

Half life of $B{i^{210}}$ is $5$ days. If we start with $50,000$ atoms of this isotope, the number of atoms left over after $10$ days is

A sample of radioactive element containing $4 \times 10^{16}$ active nuclei. Half life of element is $10$ days, then number of decayed nuclei after $30$ days is  ........ $\times 10^{16}$ 

An archaeologist analyses the wood in a prehistoric structure and finds that $C^{14}$ (Half life $= 5700\, years$) to $C^{12}$ is only one-fourth of that found in the cells of buried plants. The age of the wood is about ..........$years$

At any instant, two elements $X _1$ and $X _2$ have same number of radioactive atoms. If the decay constant of $X _1$ and $X _2$ are $10 \lambda$ and $\lambda$ respectively. then the time when the ratio of their atoms becomes $\frac{1}{e}$ respectively will be

The half-life of radium is about $1600$ years. Of $100\, g$ of radium existing now, $25\, g$ will remain unchanged after .......... $years$