The energy spectrum of $\beta$-particles [number $N(E)$ as a function of $\beta$-energy $E$] emitted from a radioactive source is
In a radioactive material the activity at time $t_1$ is $R_1$ and at a later time $t_2$ it is $R_2$. If the decay constant of the material is $\lambda$ then
The fraction $f$ of radioactive material that has decayed in time $t$, varies with time $t$. The correct variation is given by the curve
A radio isotope $X$ with a half-life $1.4 \times 10^{9}\; years$ decays of $Y$ which is stable. A sample of the rock from a cave was found to contain $X$ and $Y$ in the ratio $1: 7$. The age of the rock is ........ $ \times 10^9\; years$
Which of the following Statements is correct?
The rate of disintegration was observed to be ${10^{17}}$ disintegrations per sec when its half life period is $1445$ years. The original number of particles are