A) \[1.6\times {{10}^{10}}kg/s\]
B) \[2.3\times {{10}^{9}}kg/s\]
C) \[6.2\times {{10}^{11}}\,kg/s\]
D) \[5.5\times {{10}^{10}}\,kg/s\]
Correct Answer: C
Solution :
[c] The rate \[dm/dt\] can be calculate as; Power, \[P=\frac{dE}{dt}=\frac{dE}{dm}\times \frac{dm}{dt}=\frac{\Delta E}{\Delta m}\times \frac{dm}{dt}\] \[\therefore \,\,\,\,\,\,\,\,\,\,\frac{dm}{dt}=\frac{\Delta m}{\Delta E}P\] ?..(i) We known that \[26.2\,MeV=4.20\times {{10}^{-12}}J\] of thermal energy is produced when four protons are consumed. This is \[\Delta E=4.20\times {{10}^{-12}}J\] for \[\Delta m=4\times (1.67\times {{10}^{-27}}kg).\] Substituting these values in equation (i), we have \[\frac{dm}{dt}=\frac{\Delta m}{\Delta E}P=\frac{4(1.67\times {{10}^{-27}})}{4.20\times {{10}^{-12}}}\times (3.90\times {{10}^{26}})\] \[=6.2\times {{10}^{11}}kg/s\]
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