$A$ fraction $f_1$ of a radioactive sample decays in one mean life,and a fraction $f_2$ decays in one half-life.

The half-life of a radioactive nucleus is $5$ years. The fraction of the original sample that would decay in $15$ years is

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

$1 \, mg$ of gold undergoes decay with a $2.7 \, \text{days}$ half-life period. The amount left after $8.1 \, \text{days}$ is ......... $mg$.

$A$ radioactive nucleus $n_2$ has $3$ times the decay constant as compared to the decay constant of another radioactive nucleus $n_1$. If initial number of both nuclei are the same,what is the ratio of number of nuclei of $n_2$ to the number of nuclei of $n_1$,after one half-life of $n_1$?

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