Two radioactive isotopes $P$ and $Q$ have half Jives $10$ minutes and $15$ minutes respectively. Freshly prepared samples of each isotope initially gontain the same number of atoms. After $30$ minutes, the ratio $\frac{\text { number of atoms of } P}{\text { number of atoms of } Q}$ will be
$0.5$
$2.0$
$1.0$
$3.0$
A sample of radioactive element containing $4 \times 10^{16}$ active nuclei. Half life of element is $10$ days, then number of decayed nuclei after $30$ days is ........ $\times 10^{16}$
The count rate of $10\,g$ of radioactive material was measured at different times and this has been shown in the figure. The half life of material and the total counts (approximately) in the first half life period, respectively are
A radioactive sample with a half life of $1$ month has the label : “Activity$=2\, micro\,\,curies$ on $1-8-1991$.'' What will be its activity two months earlier ............ $micro\,\, curies$.
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 ............ $years$
Match the nuclear processes given in column $I$ with the appropriate option$(s)$ in column $II$
column $I$ | column $II$ |
$(A.)$Nuclear fusion | $(P.)$ Absorption of thermal neutrons by ${ }_{92}^{213} U$ |
$(B.)$Fission in a nuclear reactor | $(Q.)$ ${ }_{27}^{60} Co$ nucleus |
$(C.)$ $\beta$-decay | $(R.)$ Energy production in stars via hydrogen conversion to helium |
$(D.)$ $\gamma$-ray emission | $(S.)$ Heavy water |
$(T.)$ Neutrino emission |