KVPY SX SB Exam 2015 Question Paper

Carbon-II decays to boron-II according to the following formula.
$\stackrel{11}{{}_6}\mathit{C}\to \stackrel{11}{{}_5}\mathit{B}+{\mathit{e}}^{+}+{\mathit{\upsilon }}_{\mathit{e}}+0.96\mathrm{MeV}$
Assume that positrons (e${}^{+}$) produced in the decay combine with free electrons in the atmosphere and annihilate each other almost immediately. Also assume that the neutrinos $\left({\mathit{\upsilon }}_{\mathit{e}}\right)$ are massless and do not interact with the environment. At t = 0 we have 1 µg of $\stackrel{12}{{}_6}\mathit{C}$ . If the half-life of the decay process is ${\mathit{t}}_0$, the net energy produced between time t = 0 and $\mathit{t}=2{\mathit{t}}_0$ will be nearly -