Question

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. $3.66\times {10}^{14}\text{mega gram}mi{n}^{-1}$
• B. $3.66\times {10}^{16}\text{mega gram}mi{n}^{-1}$
• C. $3.66\times {10}^{15}\text{mega gram}mi{n}^{-1}$
• D. $3.66\times {10}^{10}\text{mega gram}mi{n}^{-1}$

Answer 1

The correct option is B $3.66\times {10}^{16}\text{mega gram}mi{n}^{-1}$

The fusion reaction is $4H_1^1\to H{e}_2^4$

The massdefect$\left(\Delta m\right)=0.028706amu=0.0028706\times 1.67\times {10}^{-24}=4.8\times {10}^{-27}g$

Energy from mass defect is $\Delta m{c}^2=4.8\times {10}^{-27}\times (3\times {10}^8{)}^2=4.32\times {10}^{-10}$

This is the energy per 4 hydrgen atoms fusion

Radius of sun $\left(R\right)=6.96\times {10}^{8}m$

Total Energy per minute $=2\times 4.2\times {10}^4\times 4\pi (6.96\times {10}^8)$

Let mass of hydrogen required be 4n then the energy released due to mass defect is $n\times 4.32\times {10}^{-27}$

$\Rightarrow 4n=3.66\times {10}^{16}Mg/min$