A) \[63\times {{10}^{20}}\,J\]
B) \[63\times {{10}^{14}}\,J\]
C) \[63\times {{10}^{10}}\,J\]
D) \[63\times {{10}^{7}}\,J\]
Correct Answer: C
Solution :
Key-Idea : Einstein?s mass-energy relation gives the conversion of mass into energy. If a substance loses an amount \[\Delta \,m\] of its mass, an Equivalent amount \[\Delta \,E\] of energy is produced. \[\Delta \,E=\left( \Delta m \right){{c}^{2}}\] Where \[c\] is speed of light. This is Einstein?s mass energy relation. Given, \[{{m}_{1}}=1g=1\times {{10}^{-3}}\,\,kg\] \[{{m}_{2}}=0.993g=0.993\times {{10}^{-3}}\,\,kg\] \[\therefore \]\[\Delta \,m={{m}_{1}}-{{m}_{2}}=\left( 1\times {{10}^{-3}} \right)-\left( 0.993\times {{10}^{-3}} \right)\] \[=0.007\times {{10}^{-3}}\] \[=7\times {{10}^{-6}}\,\,kg\] \[E=7\times {{10}^{-6}}\times {{\left( 3\times {{10}^{8}} \right)}^{2}}\] \[E=63\times {{10}^{10}}\,\,J\]
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