Assuming that (1) the solar luminosity has been constant since the Sun formed, and (2) the Sun was initially of uniform composition throughout, as described by Table 9.2, estimate how long it would take the Sun to convert all of its original hydrogen into helium. [Hint: Calculate the mass of hydrogen in the sun and then divide it by the rate of hydrogen fusion]

Based on the mass and luminosity of the Sun, the time required to convert of its original hydrogen into helium is 7.505 × 10^10 years.

What is nuclear fusion?

Nuclear fusion is the process whereby nucleus of lighter atoms are fused together to produce heavier atoms with the release of large amounts of energy.

Nuclear fusion occurs at the core of the sun where four hydrogen atoms are fused to form one helium atom with the release considerable energy, and this is known as hydrogen fusion.

The mass of the Sun = 2.0 × 10^30 kg

The Sun’s hydrogen mass is 0.71 × 2.0 × 10^30 kg = 1.42 × 10^30 kg.

The Sun converts 6 × 10^11 kg of hydrogen into helium per second.

Time required to convert all of the Sun's hydrogen to helium = 1.42 × 10^30 kg/6 × 10^11 kg/s

Time required = 2.367 × 10^18 seconds

Converting to years:

3.154 × 10^7 seconds = 1 year

2.367 × 10^18 seconds = 2.367 × 10^18 seconds * 1 year/3.154 × 10^7 seconds

Time required = 7.505 × 10^8 years

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