Three fourth of the active decays in a radioactive sample in $3/4\, sec$. The half life of the sample is

A radioactive sample consists of two distinct species having equal number of atoms initially. The mean life time of one species is $\tau$ and that of the other is $5 \tau$. The decay products in both cases are stable. A plot is made of the total number of radioactive nuclei as a function of time. Which of the following figures best represents the form of this plot

Starting with a sample of pure ${}^{66}Cu,\frac{7}{8}$ of it decays into $Zn$ in $15\, minutes$. The corresponding half life is……….$minutes$

A radioactive substance decays to $\left(\frac{1}{16}\right)^{t h}$ of its initial activity in $80\, days.$ The half life of the radioactive substance expressed in days is … .

Two radioactive elements $A$ and $B$ initially have same number of atoms. The half life of $A$ is same as the average life of $B$. If $\lambda_A$ and $\lambda_B$ are decay constants of $A$ and $B$ respectively, then choose the correct relation from the given options.