At what rate, in mega gram per minute, must hydrogen be consumed in fusion reaction to provide the sun with the energy it radiates? (Take mass defect per reaction to be 0.028706a.m.u)
A
3.66×1014mega grammin−1
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B
3.66×1016mega grammin−1
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C
3.66×1015mega grammin−1
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D
3.66×1010mega grammin−1
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Solution
The correct option is B3.66×1016mega grammin−1 The fusion reaction is 4H11→He42
The massdefect(Δm)=0.028706amu=0.0028706×1.67×10−24=4.8×10−27g
Energy from mass defect is Δmc2=4.8×10−27×(3×108)2=4.32×10−10
This is the energy per 4 hydrgen atoms fusion
Radius of sun (R)=6.96×108m
Total Energy per minute =2×4.2×104×4π(6.96×108)
Let mass of hydrogen required be 4n then the energy released due to mass defect is n×4.32×10−27