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Chapter 15: Problem 42

Based on the fractional mass loss associated with turning four hydrogen atoms into a helium atom, what fraction of the sun's mass would it lose over its lifetime by converting all its hydrogen into helium, under the simplifying assumption that it starts its life as \(100 \%\) hydrogen?

Short Answer

Expert verified
Answer: 0.712%

Step by step solution

01

Understand the mass loss in converting four hydrogen atoms into a helium atom

The fusion of four hydrogen atoms to make a helium atom results in a mass loss because the mass of the helium atom is slightly less than the mass of four hydrogen atoms. This mass difference is converted into energy through nuclear fusion. We will use this mass difference to calculate the fractional mass loss. The mass of a single hydrogen atom \(m_H\) is given by: \(m_H = 1.007825 u\) (atomic units) The mass of a helium atom \(m_{He}\) is given by: \(m_{He} = 4.002603 u\) (atomic units)
02

Calculate the mass difference and fractional mass loss

To determine the mass difference between four hydrogen atoms and one helium atom, we first calculate the total mass of four hydrogen atoms: \(4m_H = 4 \times 1.007825 u = 4.0313 u\) Next, we find the mass difference: \(\Delta m = 4m_H - m_{He} = 4.0313 u - 4.002603 u = 0.028697 u\) Now we can find the fractional mass loss associated with the conversion of four hydrogen atoms into a helium atom: \(fractional\_mass\_loss = \frac{\Delta m}{4m_H} = \frac{0.028697 u}{4.0313 u} = 0.00712\)
03

Calculate the fraction of the sun's mass lost over its lifetime

To find the fraction of the sun's mass lost over its lifetime by converting all its hydrogen into helium, we will assume that the sun starts its life as 100% hydrogen. Since the fractional mass loss for the conversion of four hydrogen atoms into a helium atom is 0.00712, the fraction of the sun's mass lost over its lifetime would be the same value, which is: \(fraction\_of\_mass\_lost = 0.00712\) So, the sun would lose \(0.00712 = 0.712 \%\) of its mass over its lifetime by converting all its hydrogen into helium under the simplifying assumption that it starts its life as 100% hydrogen.

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Most popular questions from this chapter

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