A) \[0.63\times {{10}^{10}}J\]
B) \[6.63\times {{10}^{14}}J\]
C) \[63\times {{10}^{10}}J\]
D) \[0.63\times {{10}^{7}}J\]
Correct Answer: B
Solution :
Einstein by its theory of relativity proved that mass and energy are related to each other. If a substance loses an amount AM of its mass, an equivalent amount \[\Delta E\]of energy is produced, where \[\Delta E=(\Delta M)\,{{c}^{2}}\] where c is velocity of light. Mass. of hydrogen, \[{{m}_{1}}=1\,g=1\times {{10}^{-3}}kg\] Mass of helium, \[{{m}_{2}}=0.993\,g=0.993\times {{10}^{-3}}kg\] \[\therefore \] \[\Delta E=[\,(1\times {{10}^{-3}})-(0.993\times {{10}^{-3}})]\] \[\times \,{{(3\times {{10}^{8}})}^{2}}\] \[\Delta E=7\times {{10}^{6}}\times 9\times {{10}^{16}}\] \[\Delta E=63\times {{10}^{10}}J\]
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