Explain decay constant and write down its definition.

The half-life of a radioactive element $A$ is the same as the mean-life of another radioactive element $B.$ Initially both substances have the same number of atoms, then

If $T$ is the half life of a radioactive material, then the fraction that would remain after a time $\frac{T}{2}$ is

Half lives of two radioactive substances $A$ and $B$ are respectively $20$ minutes and $40$ minutes. Initially the sample of $A$ and $B$ have equal number of nuclei. After $80$ minutes, the ratio of remaining number of $A$ and $B$ nuclei is

A radioactive reaction is $_{92}{U^{238}}{ \to _{82}}P{b^{206}}$. How many $\alpha $ and $\beta $  particles are emitted