Within what radius of the Sun has its original hydrogen been partially used up?
Added by Ronnie G.
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Step 1: Understand that the Sun generates energy by fusing hydrogen into helium in its core. Show more…
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Assume that the core of the Sun has one-eighth of the Sun's mass and is compressed within a sphere whose radius is one-fourth of the solar radius. Assume further that the composition of the core is 35$\%$ hydrogen by mass and that essentially all the Sun's energy is generated there. If the Sun continues to burn hydrogen at the current rate of $6.2 \times 10^{11} \mathrm{kg} / \mathrm{s}$ , how long will it be before the hydrogen is entirely consumed? The Sun's mass is $2.0 \times 10^{30} \mathrm{kg}$ .
Eduard S.
After determining that the Sun has existed for hundreds of millions of years, but before the discovery of nuclear physics, scientists could not explain why the Sun has continued to burn for such a long time. For example, if it were a coal fire, the Sun would have burned up in about 3000 yr. Assume that the Sun, whose mass is 1.99 x 1030 kg, originally consisted entirely of hydrogen and that its total power output is 3.76 x 1026 W. (a) If the energy-generating mechanism of the Sun is due to the transforming of hydrogen into helium via the following net reaction, calculate the energy (Q) given off by this reaction. (b) Determine how many hydrogen atoms constitute the Sun. Take the mass of one hydrogen atom to be 1.67 x 10-27 kg. (c) Assuming that the total power output remains constant, after what time will all the hydrogen be converted into helium, making the Sun die? The actual projected lifetime of the Sun is about 10 billion years, because only the hydrogen in a relatively small core is available as a fuel. (Only in the Sun's core are temperatures and densities high enough for the fusion reaction to be self-sustaining).
Timothy J.
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