${C^{14}}$ has half life $5700$ years. At the end of $11400$ years, the actual amount left is
$0.5$ of original amount
$0.25$ of original amount
$0.125$ of original amount
$0.0625$ of original amount
$99 \%$ of a radioactive element will decay between
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 |
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
The energy spectrum of $\beta$-particles [number $N(E)$ as a function of $\beta$-energy $E$] emitted from a radioactive source is
A radioactive element ${ }_{92}^{242} X$ emits two $\alpha$-particles, one electron and two positrons. The product nucleus is represented by ${ }_{ P }^{234} Y$. The value of $P$ is $..................$