The masses of two radioactive substances are same and their half-lives are $1 \ yr$ and $2 \ yr$ respectively. The ratio of their activities after $4 \ yr$ will be

Define the decay constant and state its $SI$ unit.

The percentage of ${}^{235}U$ presently on Earth is $0.72\%$ and the rest $(99.28\%)$ may be taken to be ${}^{238}U$. Assume that all uranium on Earth was produced in a supernova explosion long ago with the initial ratio ${}^{235}U / {}^{238}U = 2.0$. How long ago did the supernova event occur? (Take the half-lives of ${}^{235}U$ and ${}^{238}U$ to be $7.1 \times 10^8$ years and $4.5 \times 10^9$ years respectively).

Define the average life of a radioactive sample and obtain its relation to decay constant and half-life.

The variation of decay rate with the number of active nuclei is correctly shown in which graph?

For a substance,the fraction of its initial quantity $(N_0)$ which will disintegrate in its average lifetime is about $(e = 2.71)$.