question_answer

A star initially has \[{{10}^{40}}\] deutrons. It produces energy by processes, \[_{1}{{H}^{2}}+\,{{\,}_{1}}{{H}^{2}}\,\,\xrightarrow{{}}\,{{\,}_{1}}{{H}^{3}}+p\]and \[_{1}{{H}^{2}}+\,{{\,}_{1}}{{H}^{3}}\,\,\xrightarrow{{}}\,{{\,}_{2}}H{{e}^{4}}+n\]  If average power radiated by star is \[{{10}^{16}}W\] find time (in second) in which deutron is exhausted. \[\operatorname{M}{{(}_{1}}{{H}^{2}})=\,\,2.01471\,amu\], \[M{{(}_{2}}H{{e}^{4}})=400388\,\,amu\], \[{{\operatorname{m}}_{p}}= 1.00783 amu\], \[{{\operatorname{m}}_{n}}=1.00866amu\]

Answer:

\[(3.5\times {{10}^{12}})\]