The half-life of $B{i^{210}}$ is $5\, days$. What time is taken by $(7/8)^{th}$ part of the sample to decay.........$days$

Which of the following cannot be emitted by radioactive substances during their decay

The radioactive sources $A$ and $B$ of half lives of $2\, hr$ and $4\, hr$ respectively, initially contain the same number of radioactive atoms. At the end of $2\, hours,$ their rates of disintegration are in the ratio :

For a certain radioactive process the graph between $In\, {R}$ and ${t}\,({sec})$ is obtained as shown in the figure. Then the value of half life for the unknown radioactive material is approximately $....\,{sec}.$

Two radioactive materials $A$ and $B$ have decay constants $25 \lambda$ and $16 \lambda$ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of $B$ to that of $A$ will be "$e$" after a time $\frac{1}{a \lambda}$. The value of $a$ is $......$

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