A radioactive substance has a half-life of $1$ year. The fraction of this material, that would remain after $5$ years will be
$\frac{1}{{32}}$
$\frac{1}{5}$
$\frac{1}{2}$
$\frac{4}{5}$
A radioactive isotope $X$ with a half-life of $1.37 \times {10^9}$ years decays to $Y$ which is stable. A sample of rock from the moon was found to contain both the elements $X$ and $Y$ which were in the ratio of $1 : 7$. The age of the rock 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
The radioactivity of a given sample of whisky due to tritium (half life $12.3$ years) was found to be only $3\%$ of that measured in a recently purchased bottle marked $"7$ years old". The sample must have been prepared about
The mean life of a radioactive sample are $30\,year$ and $60\,year$ for $\alpha -$ emission and $\beta -$ emission respectively. If the sample decays both by $\alpha -$ emission and $\beta -$ emission simultaneously, then the time after which, only one-fourth of the sample remain is approximately ............ $years$
A radioactive sample is undergoing $\alpha$ decay. At any time $t_{1}$, its activity is $A$ and another time $t _{2}$, the activity is $\frac{ A }{5}$. What is the average life time for the sample?