The half life of a radioactive substance against $\alpha - $ decay is $1.2 \times 10^7\, s$. What is the decay rate for $4.0 \times 10^{15}$ atoms of the substance
$4.6 \times {10^{12}}\,atoms/s$
$2.3 \times {10^{11}}\,atoms/s$
$4.6 \times {10^{10}}\,atoms/s$
$2.3 \times {10^{8}}\,atoms/s$
The decay constants of a radioactive substance for $\alpha $ and $\beta $ emission are ${\lambda _\alpha }$ and ${\lambda _\beta }$ respectively. If the substance emits $\alpha $ and $\beta $ simultaneously, then the average half life of the material will be
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
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
In a radioactive decay chain, ${ }_{90}^{232} Th$ nucleus decays to ${ }_{82}^{212} Pb$ nucleus. Let $N _\alpha$ and $N _\beta$ be the number of $\alpha$ and $\beta^{-}$particles, respectively, emitted in this decay process. Which of the following statements is (are) true?
$(A)$ $N _\alpha=5$ $(B)$ $N _\alpha=6$ $(C)$ $N _\beta=2$ $(D)$ $N _\beta=4$
Write the definition and unit of decay constant.