Chapter 12, Problem 39QAP

(a)

To determine

The percentage of hydrogen in the core originally.

Answer to Problem 39QAP

The percentage of hydrogen was $70\text{percent}$ of total mass in the core originally.

Explanation of Solution

Sun is middle-aged, main sequence star of G2 spectral type. The surface temperature of the Sun is 5800 K. It continuously produces energy with the help of nuclear fusion occurring in its core that is transferred from its core to outer surface.

The sun had even mass composition of helium and hydrogen throughout its core and surface when it was formed. Helium was $30\text{percent}$ and hydrogen was $70\text{percent}$ at the time of formation of the Sun.

Conclusion:

Thus, the percentage of hydrogen was $70\text{percent}$ of total mass in the core originally.

(b)

To determine

The percentage of hydrogen in the core today.

Answer to Problem 39QAP

The percentage of hydrogen is $35\text{percent}$ of total mass in the core today.

Explanation of Solution

Sun is middle-aged, main sequence star of G2 spectral type. The surface temperature of the Sun is 5800 K. It continuously produces energy with the help of nuclear fusion occurring in its core that is transferred from its core to outer surface.

The sun had even mass composition of helium and hydrogen throughout its core and surface when it was formed. Helium was $30\text{percent}$ and hydrogen was $70\text{percent}$ at the time of formation of the Sun.

However, continuous fusion of hydrogen atoms into helium decreases the amount of hydrogen in the core. Today, only $35\text{percent}$ of total mass is hydrogen and $65\text{percent}$ of total mass is helium.

Conclusion:

Thus, the percentage of hydrogen is $35\text{percent}$ of total mass in the core today.

(c)

To determine

The percentage of hydrogen in the core originally.

Answer to Problem 39QAP

The percentage of hydrogen will zero percent of total mass in the core after $5\text{billion years}$ from now.

Explanation of Solution

Sun is middle-aged, main sequence star of G2 spectral type. The surface temperature of the Sun is 5800 K. It continuously produces energy with the help of nuclear fusion occurring in its core that is transferred from its core to outer surface.

The sun had even mass composition of helium and hydrogen throughout its core and surface when it was formed. Helium was $30\text{percent}$ and hydrogen was $70\text{percent}$ at the time of formation of the Sun.

However, continuous fusion of hydrogen atoms into helium decreases the amount of hydrogen in the core. Today, only $35\text{percent}$ of total mass is hydrogen and $65\text{percent}$ of total mass is helium.

The lifetime of Sun is $10\text{billion years}$; out of which it has spent already $5\text{billion years}$. The continuous fusion will result into zero percent of hydrogen in the core after $5\text{billion years}$ form now.

Conclusion:

Thus, the percentage of hydrogen will zero percent of total mass in the core after $5\text{billion years}$ from now.

(d)

To determine

The percentage of hydrogen in the entire Sun originally.

Answer to Problem 39QAP

The percentage of hydrogen was $70\text{percent}$ of total mass in the entire Sun originally.

Explanation of Solution

Sun is middle-aged, main sequence star of G2 spectral type. The surface temperature of the Sun is 5800 K. It continuously produces energy with the help of nuclear fusion occurring in its core that is transferred from its core to outer surface.

The sun had even mass composition of helium and hydrogen throughout its core and surface when it was formed. Helium was $30\text{percent}$ and hydrogen was $70\text{percent}$ at the time of formation of the Sun.

Conclusion:

Thus, the percentage of hydrogen was $70\text{percent}$ of total mass in the entire Sun originally.

(e)

To determine

The percentage of hydrogen in the core today.

Answer to Problem 39QAP

The percentage of hydrogen is $66\text{percent}$ of total mass in the entire Sun today.

Explanation of Solution

Sun is middle-aged, main sequence star of G2 spectral type. The surface temperature of the Sun is 5800 K. It continuously produces energy with the help of nuclear fusion occurring in its core that is transferred from its core to outer surface.

The sun had even mass composition of helium and hydrogen throughout its core and surface when it was formed. Helium was $30\text{percent}$ and hydrogen was $70\text{percent}$ at the time of formation of the Sun.

However, continuous fusion of hydrogen atoms into helium decreases the amount of hydrogen in the core. Today, only $35\text{percent}$ of total mass is hydrogen and $65\text{percent}$ of total mass is helium.

The core of the Sun extends up to $0.2$ times the size of the Sun; composition of the Sun in remaining surface is still the same; it means the ratio of hydrogen and helium amount in outer $80\text{percent}$ has not changed and only inner $20\text{percent}$ is changed.

From figure, it is observed that $66\text{percent}$ is hydrogen and $34\text{percent}$ is helium of total mass in the entire Sun.

Conclusion:

Thus, the percentage of hydrogen is $66\text{percent}$ of total mass in the entire Sun today.

(f)

To determine

The percentage of hydrogen in the core originally.

Answer to Problem 39QAP

The percentage of hydrogen is $62\text{percent}$ of total mass in the entire Sun today.

Explanation of Solution

Sun is middle-aged, main sequence star of G2 spectral type. The surface temperature of the Sun is 5800 K. It continuously produces energy with the help of nuclear fusion occurring in its core that is transferred from its core to outer surface.

The sun had even mass composition of helium and hydrogen throughout its core and surface when it was formed. Helium was $30\text{percent}$ and hydrogen was $70\text{percent}$ at the time of formation of the Sun.

However, continuous fusion of hydrogen atoms into helium decreases the amount of hydrogen in the core. Today, only $35\text{percent}$ of total mass is hydrogen and $65\text{percent}$ of total mass is helium.

The lifetime of Sun is $10\text{billion years}$; out of which it has spent already $5\text{billion years}$. The continuous fusion will result into zero percent of hydrogen in the core after $5\text{billion years}$ form now.

The core of the Sun extends up to $0.2$ times the size of the Sun; composition of the Sun in remaining surface is still the same; it means the ratio of hydrogen and helium amount in outer $80\text{percent}$ has not changed and only inner $20\text{percent}$ is changed.

From figure, it is observed that $62\text{percent}$ is hydrogen and $38\text{percent}$ is helium of total mass in the entire Sun.

Conclusion:

Thus, the percentage of hydrogen is $62\text{percent}$ of total mass in the entire Sun today.