The sun produces energy via nuclear fusion at the rate of 4 x10^26J/s . Based on

Question

The sun produces energy via nuclear fusion at the rate of 4 x10^26J/s . Based on the proposed overall fusion equation, how long will the sun shine in years before it exhausts its hydrogen fuel? (Assume that there are 365 days in the average year.) Express your answer to one significant figure and include the appropriate units.

Proposed solar fusion reaction

Spectroscopic studies have shown that the fusion reaction in the sun's core proceeds by a complicated mechanism. One proposed overall equation for the solar fusion reaction is

411H+2 0?1e?42He

which is also accompanied by the release of "massless" neutrinos and photons in addition to energy. Precise masses of the reactants and product are given below.

Explanation / Answer

4(1.007825) + 2(0.00549) - 4.002603 = 0.029795 amu is the energy from hydrogen gas.

4.0313 amu H+ > 0.029795 amu = ratio of 1 to 0.00739

dE = ((2*10^30 kg) x 0.8 x 0.25)(3.00x10^8 m/s)^2 = 3.6x10^46 kg x m^2/s^2

3.6x10^46 kg x m^2/s^2 x 0.00739 = 2.6604 x 60^44 kg x m^2/s^2

4x10^26 J/s x s = 2.6604x10^44 kg x m^2/s^2 solve for s.
s = 6.651x10^17 seconds

6.651x10^17 seconds x 1 min/60 s x 1 hr/ 60 min x 1 day/ 24 hr x 1 yr / 365 days = 2.1x10^10 years

2X10^10 years is your answer..

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