If the Sun converts 5 × 10¹¹ kg of H to He per second and the mass of a single hydrogen nucleus is 1.7 × 10⁻²⁷ kg,how many net proton-proton reactions go on per second in the Sun? What is the luminosity produced if the mass difference between a single helium nucleus and four hydrogen nuclei is 4 × 10⁻²⁹ kg? Note that 1 Watt = 1 m² kg/s³.

Question

Quizplus · Accepted Answer

To calculate the net proton-proton reactions per second, we need to first calculate the number of helium nuclei produced per second:

Mass of 4 hydrogen nuclei = 4 x 1.67 x 10^-27 kg = 6.68 x 10^-27 kg
Mass of 1 helium nucleus = 6.64 x 10^-27 kg
Mass difference = 6.68 x 10^-27 kg - 6.64 x 10^-27 kg = 4 x 10^-29 kg

Luminosity produced = mass difference x H to He conversion rate
Luminosity produced = 4 x 10^-29 kg x 5 x 10^11 kg/s
Luminosity produced = 2 x 10^-17 W

To calculate the net proton-proton reactions per second, we use the fact that each reaction produces one helium nucleus:

H + H -> He + energy

Mass of two hydrogen nuclei = 2 x 1.67 x 10^-27 kg = 3.34 x 10^-27 kg

Net reactions per second = H to He conversion rate / (mass of two hydrogen nuclei)
Net reactions per second = 5 x 10^11 kg/s / 3.34 x 10^-27 kg
Net reactions per second = 1.5 x 10^38 reactions/s

Therefore, the best choice is A: 7 x 10^37 reactions per sec; 3 x 10^26 Watt.

If the Sun Converts 5 × 1011 Kg of H

If the Sun Converts 5 × 10¹¹ Kg of H