The half-life of radium is $1600 \, \text{years}$. After how many years will $25 \, \text{g}$ of radium remain from $100 \, \text{g}$ of radium?

$A$ radioactive material decays by simultaneous emission of two particles with respective half-lives $1620$ years and $810$ years. The time (in years) after which one-fourth of the material remains is:

The graph which represents the correct variation of logarithm of activity $(\log A)$ versus time $t$ is:

$A$ radioactive substance has a half-life of $60\, minutes$. After $3\, hours$,the fraction of atoms that have decayed would be ......... $\%$

There are two radionuclei $A$ and $B.$ $A$ is an alpha emitter and $B$ is a beta emitter. Their disintegration constants are in the ratio of $1 : 2.$ What should be the ratio of the number of atoms of the two at time $t = 0$ so that the probabilities of getting $\alpha$ and $\beta$ particles are the same at time $t = 0$?

Ten percent of a radioactive sample has decayed in $1$ day. After $2$ days,the decayed percentage of nuclei will be ...... $\%$