A radioactive element $$X$$ convents into another stable element $$Y$$. Half-life of $$X$$ is 2 hrs. Initially only $$X$$ is present. After time $$t$$, the ratio of atoms of $$X$$ and $$Y$$ is found to be $$1: 4$$, then $$t$$ in hours is

A nuclide at rest emits an $\alpha$-particle. In this process

The half-life period of a radioactive element $$x$$ is same as the mean life time of another radioactive element $$y$$. Initially, both of them have the same number of atoms. Then,

Polonium has a half-life of 140 days. If we take $$20 \mathrm{~g}$$ of polonium initially then the amount of it that remains after 280 days is