A) \[9\times {{10}^{19}}\,\,J\]
B) \[9\times {{10}^{17}}\,\,J\]
C) \[9\times {{10}^{16}}\,\,J\]
D) \[9\times {{10}^{13}}\,\,J\]
Correct Answer: D
Solution :
Key-Idea: Mass can be converted into energy using mass-energy equivalence. If a substance loses an amount \[\Delta \,m\] of its mass, an equivalent amount \[\Delta \,E\] of energy is produced, where \[\Delta E=\left( \Delta \,\,m \right)\,{{c}^{2}}\] Where \[c\] is speed of light. This is called Einstein?s mass energy relation. Amount of mass converted into energy is, \[\Delta \,m=\frac{0.1}{100}\times 1={{10}^{-3}}\,\,kg\] and \[c=3\times {{10}^{8}}\,\,m/s\] \[\therefore \] \[\Delta \,E={{10}^{-3}}\times {{\left( 3\times {{10}^{8}} \right)}^{2}}\] \[\Delta \,E=9\times {{10}^{13}}\,J\]
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