Concept explainers
The fraction of the Sun’s mass that will be converted into helium over the next 5 billion years, if it is assumed that the current rate of the hydrogen fusion remains constant. Also, discuss its effect on the overall chemical composition of the Sun.
Answer to Problem 10Q
Solution:
Explanation of Solution
Given data:
The current rate of the hydrogen fusion in the Sun remains constant.
The time is 5 billion year.
Formula used:
The expression for the mass-energy equation is written as:
Here, E is the total energy radiated, m is the mass of object, and c is the
Explanation:
The Sun’s luminosity is
The total energy radiated by the Sun in 5 billion year is calculated as,
Recall the expression of the mass-energy equation.
Rearrange the above expression for
Substitute
Only .7% of the mass is transformed into energy at the time of conversion of the hydrogen into helium. So, the amount of hydrogen used in Sun’s energy production over the next 5 billion year is,
The mass of the Sun is
The present composition of the Sun is 74% hydrogen, 25% helium, and 1% heavy elements.
Thus, the mass of each component in Sun is,
The mass of hydrogen is,
The mass of helium is,
The mass of heavy elements is,
Over 5 billion year the composition of the Sun is as:
The composition of hydrogen is,
The fraction of the sun’s mass that will be hydrogen in 5 billion year is,
It is 69% of the Sun’s mass.
Now, the composition of helium is,
The fraction of the sun’s mass that will be helium in 5 billion year is,
It is 30% of the Sun’s mass.
Conclusion:
Therefore, the mass converted into energy in 5 billion year is
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Chapter 16 Solutions
Universe
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