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

The half-life period of a radioactive sample is $T$. If a fraction $x$ disintegrates in time $t$,what fraction will decay in time $\frac{t}{2}$?

Write the definition of half-life of a radioactive substance and obtain its relation to the decay constant.

$A$ freshly prepared radioactive source of half-life $2$ hours $30$ minutes emits radiation which is $64$ times the permissible safe level. The minimum time,after which it would be possible to work safely with the source,will be in hours.

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

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).