A radioactive sample decays $\frac{7}{4}$ times its original quantity in $15$ minutes. The half-life of the sample is $......min$

In a mean life of a radioactive sample

A source contains two phosphorous radio nuclides $_{15}^{32} P \left(T_{1 / 2}=14.3 d \right)$ and $_{15}^{33} P \left(T_{1 / 2}=25.3 d \right) .$ Initially, $10 \%$ of the decays come from $_{15}^{33} P$ How long one must wait until $90 \%$ do so?

The mean lives of a radioactive sample are $30$ years and $60$ years for $\alpha$-emission and $\beta $ -emission respectively. If the sample decays both by $\alpha$- emission and $\beta $-emission simultaneously, the time after which, only one-fourth of the sample remain is :- ........... $years$

A piece of wood from the ruins of an ancient building was found to have a $^{14}C$ activity of $12$ disintegrations per minute per gram of its carbon content. The $^{14}C$ activity of the living wood is $16$ disintegrations per minute per gram. How long ago did the tree, from which the wooden sample came, die? Given half-life of $^{14}C$ is $5760$ years.

The half-life of a sample of a radioactive substance is $1$ hour. If $8 \times {10^{10}}$ atoms are present at $t = 0$, then the number of atoms decayed in the duration $t = 2$ hour to $t = 4$ hour will be