The time for which the sun must shine in order to release energy produced by the mass-energy conversion of a carbon atom with mass 2 × 10 − 26 kg . The sun’s luminosity is 3.90 × 10 26 W .

Question

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Answer 1

Question

Chapter 16, Problem 9Q

(a)

To determine

The time for which the sun must shine in order to release energy produced by the mass-energy conversion of a carbon atom with mass $2×10−26 kg$ . The sun’s luminosity is $3.90×1026 W$ .

(a)

Expert Solution

Answer to Problem 9Q

Solution:

$4.6×10−36 s$

Explanation of Solution

Given data:

The sun’s luminosity is $3.90×1026 W$ , and the mass of carbon atom is $2×10−26 kg$ .

Formula used:

Time taken in seconds is given as:

$t=EL⊙$

Here, $E$ is the energy released due to mass-energy equivalence in joule and $L⊙$ is the luminosity in joule per second.

Einstein’s mass-energy conversion:

$E=mc2$

Where, E is the energy release from the mass of m and c is speed of light.

Explanation:

Calculating the energy released mass-energy conversion of a carbon atom:

$E=mc2$

Replace $2×10−26 kg$ for m and $3×108 m/s2$ for c in the above equation:

$E=(2×10−26 kg)(3×108 m/s2)2=1.8×10−9 J$

Recalling the expression for time:

$t=EL⊙$

Substituting $1.8×10−9 J$ for $E$ and $3.90×1026 W$ for $L⊙$ in the above expression:

$t=1.8×10−9 J3.90×1026 Jsecond =4.6×10−36 seconds$

Conclusion:

The sun must shine $4.6×10−36 s$ to produce the energy produced by a carbon atom with mass $2×10−26 kg$ .

(b)

To determine

The time for which the sun must shine in order to release energy produced by the mass-energy conversion of 1 kg substance. The sun’s luminosity is $3.90×1026 W$ .

(b)

Expert Solution

Answer to Problem 9Q

Solution:

$2.3×10−10 s$

Explanation of Solution

Given data:

The sun’s luminosity is $3.90×1026 W$ , and the mass of the substance is 1 kg.

Formula used:

Time taken in seconds is given as:

$t=EL⊙$

Here, $E$ is the energy released due to mass-energy equivalence in joule and $L⊙$ is the luminosity in joule per second.

Einstein’s mass-energy conversion:

$E=mc2$

Where, E is the energy release from the mass of m and c is speed of light.

Explanation:

Calculating the energy released mass-energy conversion of a carbon atom:

$E=mc2$

Replace $1 kg$ for m and $3×108 m/s2$ for c in the above equation:

$E=(1 kg)(3×108 m/s2)2=9×1016 J$

Recalling the expression for the time:

$t=EL⊙$

Substituting $9.1×1016 J$ for $E$ and $3.90×1026 W$ for $L⊙$ in the above expression:

$t=9.1×1016 J 3.90×1026 Jsecond =2.3×10−10 seconds$

Conclusion:

The sun must shine for $2.3×10−10 seconds$ to produce the energy produced by a substance with mass $1 kg$ .

(c)

To determine

The time for which the sun must shine in order to release energy, produced by the mass-energy conversion of Earth with mass $6×1024 kg$ . The sun’s luminosity is $3.90×1026 W$ .

(c)

Expert Solution

Answer to Problem 9Q

Solution:

$1.4×1015 seconds$

Explanation of Solution

Given data:

The sun’s luminosity is $3.90×1026 W$ , and the mass of Earth is $6×1024 kg$ .

Formula used:

Time taken in seconds is given as:

$t=EL⊙$

Here, $E$ is the energy released due to mass-energy equivalence in joule and $L⊙$ is the luminosity in joule per second.

Einstein’s mass-energy conversion:

$E=mc2$

Where, E is the energy release from the mass of m and c is speed of light.

Explanation:

Calculating the energy released mass-energy conversion of a carbon atom:

$E=mc2$

Replace $6×1024 kg$ for m and $3×108 m/s2$ for c in the above equation:

$E=(6×1024 kg)(3×108 m/s2)2=5.4×1041 J$

Recalling the expression for time:

$t=EL⊙$

Substituting $5.4×1041 J$ for $E$ and $3.90×1026 W$ for $L⊙$ in the above expression:

$t=5.4×1041 J3.90×1026 Jsecond =1.4×1015 seconds$

Conclusion:

The sun must shine for $1.4×1015 seconds$ to produce the energy produced by a substance with mass $6×1024 kg$ .

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Answer 2

Question

Chapter 16, Problem 9Q

(a)

To determine

The time for which the sun must shine in order to release energy produced by the mass-energy conversion of a carbon atom with mass $2×10−26 kg$ . The sun’s luminosity is $3.90×1026 W$ .

(a)

Expert Solution

Answer to Problem 9Q

Solution:

$4.6×10−36 s$

Explanation of Solution

Given data:

The sun’s luminosity is $3.90×1026 W$ , and the mass of carbon atom is $2×10−26 kg$ .

Formula used:

Time taken in seconds is given as:

$t=EL⊙$

Here, $E$ is the energy released due to mass-energy equivalence in joule and $L⊙$ is the luminosity in joule per second.

Einstein’s mass-energy conversion:

$E=mc2$

Where, E is the energy release from the mass of m and c is speed of light.

Explanation:

Calculating the energy released mass-energy conversion of a carbon atom:

$E=mc2$

Replace $2×10−26 kg$ for m and $3×108 m/s2$ for c in the above equation:

$E=(2×10−26 kg)(3×108 m/s2)2=1.8×10−9 J$

Recalling the expression for time:

$t=EL⊙$

Substituting $1.8×10−9 J$ for $E$ and $3.90×1026 W$ for $L⊙$ in the above expression:

$t=1.8×10−9 J3.90×1026 Jsecond =4.6×10−36 seconds$

Conclusion:

The sun must shine $4.6×10−36 s$ to produce the energy produced by a carbon atom with mass $2×10−26 kg$ .

(b)

To determine

The time for which the sun must shine in order to release energy produced by the mass-energy conversion of 1 kg substance. The sun’s luminosity is $3.90×1026 W$ .

(b)

Expert Solution

Answer to Problem 9Q

Solution:

$2.3×10−10 s$

Explanation of Solution

Given data:

The sun’s luminosity is $3.90×1026 W$ , and the mass of the substance is 1 kg.

Formula used:

Time taken in seconds is given as:

$t=EL⊙$

Here, $E$ is the energy released due to mass-energy equivalence in joule and $L⊙$ is the luminosity in joule per second.

Einstein’s mass-energy conversion:

$E=mc2$

Where, E is the energy release from the mass of m and c is speed of light.

Explanation:

Calculating the energy released mass-energy conversion of a carbon atom:

$E=mc2$

Replace $1 kg$ for m and $3×108 m/s2$ for c in the above equation:

$E=(1 kg)(3×108 m/s2)2=9×1016 J$

Recalling the expression for the time:

$t=EL⊙$

Substituting $9.1×1016 J$ for $E$ and $3.90×1026 W$ for $L⊙$ in the above expression:

$t=9.1×1016 J 3.90×1026 Jsecond =2.3×10−10 seconds$

Conclusion:

The sun must shine for $2.3×10−10 seconds$ to produce the energy produced by a substance with mass $1 kg$ .

(c)

To determine

The time for which the sun must shine in order to release energy, produced by the mass-energy conversion of Earth with mass $6×1024 kg$ . The sun’s luminosity is $3.90×1026 W$ .

(c)

Expert Solution

Answer to Problem 9Q

Solution:

$1.4×1015 seconds$

Explanation of Solution

Given data:

The sun’s luminosity is $3.90×1026 W$ , and the mass of Earth is $6×1024 kg$ .

Formula used:

Time taken in seconds is given as:

$t=EL⊙$

Here, $E$ is the energy released due to mass-energy equivalence in joule and $L⊙$ is the luminosity in joule per second.

Einstein’s mass-energy conversion:

$E=mc2$

Where, E is the energy release from the mass of m and c is speed of light.

Explanation:

Calculating the energy released mass-energy conversion of a carbon atom:

$E=mc2$

Replace $6×1024 kg$ for m and $3×108 m/s2$ for c in the above equation:

$E=(6×1024 kg)(3×108 m/s2)2=5.4×1041 J$

Recalling the expression for time:

$t=EL⊙$

Substituting $5.4×1041 J$ for $E$ and $3.90×1026 W$ for $L⊙$ in the above expression:

$t=5.4×1041 J3.90×1026 Jsecond =1.4×1015 seconds$

Conclusion:

The sun must shine for $1.4×1015 seconds$ to produce the energy produced by a substance with mass $6×1024 kg$ .

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Answer 3

Question

Chapter 16, Problem 9Q

(a)

To determine

The time for which the sun must shine in order to release energy produced by the mass-energy conversion of a carbon atom with mass $2×10−26 kg$ . The sun’s luminosity is $3.90×1026 W$ .

(a)

Expert Solution

Answer to Problem 9Q

Solution:

$4.6×10−36 s$

Explanation of Solution

Given data:

The sun’s luminosity is $3.90×1026 W$ , and the mass of carbon atom is $2×10−26 kg$ .

Formula used:

Time taken in seconds is given as:

$t=EL⊙$

Here, $E$ is the energy released due to mass-energy equivalence in joule and $L⊙$ is the luminosity in joule per second.

Einstein’s mass-energy conversion:

$E=mc2$

Where, E is the energy release from the mass of m and c is speed of light.

Explanation:

Calculating the energy released mass-energy conversion of a carbon atom:

$E=mc2$

Replace $2×10−26 kg$ for m and $3×108 m/s2$ for c in the above equation:

$E=(2×10−26 kg)(3×108 m/s2)2=1.8×10−9 J$

Recalling the expression for time:

$t=EL⊙$

Substituting $1.8×10−9 J$ for $E$ and $3.90×1026 W$ for $L⊙$ in the above expression:

$t=1.8×10−9 J3.90×1026 Jsecond =4.6×10−36 seconds$

Conclusion:

The sun must shine $4.6×10−36 s$ to produce the energy produced by a carbon atom with mass $2×10−26 kg$ .

(b)

To determine

The time for which the sun must shine in order to release energy produced by the mass-energy conversion of 1 kg substance. The sun’s luminosity is $3.90×1026 W$ .

(b)

Expert Solution

Answer to Problem 9Q

Solution:

$2.3×10−10 s$

Explanation of Solution

Given data:

The sun’s luminosity is $3.90×1026 W$ , and the mass of the substance is 1 kg.

Formula used:

Time taken in seconds is given as:

$t=EL⊙$

Here, $E$ is the energy released due to mass-energy equivalence in joule and $L⊙$ is the luminosity in joule per second.

Einstein’s mass-energy conversion:

$E=mc2$

Where, E is the energy release from the mass of m and c is speed of light.

Explanation:

Calculating the energy released mass-energy conversion of a carbon atom:

$E=mc2$

Replace $1 kg$ for m and $3×108 m/s2$ for c in the above equation:

$E=(1 kg)(3×108 m/s2)2=9×1016 J$

Recalling the expression for the time:

$t=EL⊙$

Substituting $9.1×1016 J$ for $E$ and $3.90×1026 W$ for $L⊙$ in the above expression:

$t=9.1×1016 J 3.90×1026 Jsecond =2.3×10−10 seconds$

Conclusion:

The sun must shine for $2.3×10−10 seconds$ to produce the energy produced by a substance with mass $1 kg$ .

(c)

To determine

The time for which the sun must shine in order to release energy, produced by the mass-energy conversion of Earth with mass $6×1024 kg$ . The sun’s luminosity is $3.90×1026 W$ .

(c)

Expert Solution

Answer to Problem 9Q

Solution:

$1.4×1015 seconds$

Explanation of Solution

Given data:

The sun’s luminosity is $3.90×1026 W$ , and the mass of Earth is $6×1024 kg$ .

Formula used:

Time taken in seconds is given as:

$t=EL⊙$

Here, $E$ is the energy released due to mass-energy equivalence in joule and $L⊙$ is the luminosity in joule per second.

Einstein’s mass-energy conversion:

$E=mc2$

Where, E is the energy release from the mass of m and c is speed of light.

Explanation:

Calculating the energy released mass-energy conversion of a carbon atom:

$E=mc2$

Replace $6×1024 kg$ for m and $3×108 m/s2$ for c in the above equation:

$E=(6×1024 kg)(3×108 m/s2)2=5.4×1041 J$

Recalling the expression for time:

$t=EL⊙$

Substituting $5.4×1041 J$ for $E$ and $3.90×1026 W$ for $L⊙$ in the above expression:

$t=5.4×1041 J3.90×1026 Jsecond =1.4×1015 seconds$

Conclusion:

The sun must shine for $1.4×1015 seconds$ to produce the energy produced by a substance with mass $6×1024 kg$ .

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Answer 4

Question

Chapter 16, Problem 9Q

(a)

To determine

The time for which the sun must shine in order to release energy produced by the mass-energy conversion of a carbon atom with mass $2×10−26 kg$ . The sun’s luminosity is $3.90×1026 W$ .

(a)

Expert Solution

Answer to Problem 9Q

Solution:

$4.6×10−36 s$

Explanation of Solution

Given data:

The sun’s luminosity is $3.90×1026 W$ , and the mass of carbon atom is $2×10−26 kg$ .

Formula used:

Time taken in seconds is given as:

$t=EL⊙$

Here, $E$ is the energy released due to mass-energy equivalence in joule and $L⊙$ is the luminosity in joule per second.

Einstein’s mass-energy conversion:

$E=mc2$

Where, E is the energy release from the mass of m and c is speed of light.

Explanation:

Calculating the energy released mass-energy conversion of a carbon atom:

$E=mc2$

Replace $2×10−26 kg$ for m and $3×108 m/s2$ for c in the above equation:

$E=(2×10−26 kg)(3×108 m/s2)2=1.8×10−9 J$

Recalling the expression for time:

$t=EL⊙$

Substituting $1.8×10−9 J$ for $E$ and $3.90×1026 W$ for $L⊙$ in the above expression:

$t=1.8×10−9 J3.90×1026 Jsecond =4.6×10−36 seconds$

Conclusion:

The sun must shine $4.6×10−36 s$ to produce the energy produced by a carbon atom with mass $2×10−26 kg$ .

(b)

To determine

The time for which the sun must shine in order to release energy produced by the mass-energy conversion of 1 kg substance. The sun’s luminosity is $3.90×1026 W$ .

(b)

Expert Solution

Answer to Problem 9Q

Solution:

$2.3×10−10 s$

Explanation of Solution

Given data:

The sun’s luminosity is $3.90×1026 W$ , and the mass of the substance is 1 kg.

Formula used:

Time taken in seconds is given as:

$t=EL⊙$

Here, $E$ is the energy released due to mass-energy equivalence in joule and $L⊙$ is the luminosity in joule per second.

Einstein’s mass-energy conversion:

$E=mc2$

Where, E is the energy release from the mass of m and c is speed of light.

Explanation:

Calculating the energy released mass-energy conversion of a carbon atom:

$E=mc2$

Replace $1 kg$ for m and $3×108 m/s2$ for c in the above equation:

$E=(1 kg)(3×108 m/s2)2=9×1016 J$

Recalling the expression for the time:

$t=EL⊙$

Substituting $9.1×1016 J$ for $E$ and $3.90×1026 W$ for $L⊙$ in the above expression:

$t=9.1×1016 J 3.90×1026 Jsecond =2.3×10−10 seconds$

Conclusion:

The sun must shine for $2.3×10−10 seconds$ to produce the energy produced by a substance with mass $1 kg$ .

(c)

To determine

The time for which the sun must shine in order to release energy, produced by the mass-energy conversion of Earth with mass $6×1024 kg$ . The sun’s luminosity is $3.90×1026 W$ .

(c)

Expert Solution

Answer to Problem 9Q

Solution:

$1.4×1015 seconds$

Explanation of Solution

Given data:

The sun’s luminosity is $3.90×1026 W$ , and the mass of Earth is $6×1024 kg$ .

Formula used:

Time taken in seconds is given as:

$t=EL⊙$

Here, $E$ is the energy released due to mass-energy equivalence in joule and $L⊙$ is the luminosity in joule per second.

Einstein’s mass-energy conversion:

$E=mc2$

Where, E is the energy release from the mass of m and c is speed of light.

Explanation:

Calculating the energy released mass-energy conversion of a carbon atom:

$E=mc2$

Replace $6×1024 kg$ for m and $3×108 m/s2$ for c in the above equation:

$E=(6×1024 kg)(3×108 m/s2)2=5.4×1041 J$

Recalling the expression for time:

$t=EL⊙$

Substituting $5.4×1041 J$ for $E$ and $3.90×1026 W$ for $L⊙$ in the above expression:

$t=5.4×1041 J3.90×1026 Jsecond =1.4×1015 seconds$

Conclusion:

The sun must shine for $1.4×1015 seconds$ to produce the energy produced by a substance with mass $6×1024 kg$ .

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 16, Problem 9Q

(a)

To determine

The time for which the sun must shine in order to release energy produced by the mass-energy conversion of a carbon atom with mass $2×10−26 kg$ . The sun’s luminosity is $3.90×1026 W$ .

(a)

Expert Solution

Answer to Problem 9Q

Solution:

$4.6×10−36 s$

Explanation of Solution

Given data:

The sun’s luminosity is $3.90×1026 W$ , and the mass of carbon atom is $2×10−26 kg$ .

Formula used:

Time taken in seconds is given as:

$t=EL⊙$

Here, $E$ is the energy released due to mass-energy equivalence in joule and $L⊙$ is the luminosity in joule per second.

Einstein’s mass-energy conversion:

$E=mc2$

Where, E is the energy release from the mass of m and c is speed of light.

Explanation:

Calculating the energy released mass-energy conversion of a carbon atom:

$E=mc2$

Replace $2×10−26 kg$ for m and $3×108 m/s2$ for c in the above equation:

$E=(2×10−26 kg)(3×108 m/s2)2=1.8×10−9 J$

Recalling the expression for time:

$t=EL⊙$

Substituting $1.8×10−9 J$ for $E$ and $3.90×1026 W$ for $L⊙$ in the above expression:

$t=1.8×10−9 J3.90×1026 Jsecond =4.6×10−36 seconds$

Conclusion:

The sun must shine $4.6×10−36 s$ to produce the energy produced by a carbon atom with mass $2×10−26 kg$ .

(b)

To determine

The time for which the sun must shine in order to release energy produced by the mass-energy conversion of 1 kg substance. The sun’s luminosity is $3.90×1026 W$ .

(b)

Expert Solution

Answer to Problem 9Q

Solution:

$2.3×10−10 s$

Explanation of Solution

Given data:

The sun’s luminosity is $3.90×1026 W$ , and the mass of the substance is 1 kg.

Formula used:

Time taken in seconds is given as:

$t=EL⊙$

Here, $E$ is the energy released due to mass-energy equivalence in joule and $L⊙$ is the luminosity in joule per second.

Einstein’s mass-energy conversion:

$E=mc2$

Where, E is the energy release from the mass of m and c is speed of light.

Explanation:

Calculating the energy released mass-energy conversion of a carbon atom:

$E=mc2$

Replace $1 kg$ for m and $3×108 m/s2$ for c in the above equation:

$E=(1 kg)(3×108 m/s2)2=9×1016 J$

Recalling the expression for the time:

$t=EL⊙$

Substituting $9.1×1016 J$ for $E$ and $3.90×1026 W$ for $L⊙$ in the above expression:

$t=9.1×1016 J 3.90×1026 Jsecond =2.3×10−10 seconds$

Conclusion:

The sun must shine for $2.3×10−10 seconds$ to produce the energy produced by a substance with mass $1 kg$ .

(c)

To determine

The time for which the sun must shine in order to release energy, produced by the mass-energy conversion of Earth with mass $6×1024 kg$ . The sun’s luminosity is $3.90×1026 W$ .

(c)

Expert Solution

Answer to Problem 9Q

Solution:

$1.4×1015 seconds$

Explanation of Solution

Given data:

The sun’s luminosity is $3.90×1026 W$ , and the mass of Earth is $6×1024 kg$ .

Formula used:

Time taken in seconds is given as:

$t=EL⊙$

Here, $E$ is the energy released due to mass-energy equivalence in joule and $L⊙$ is the luminosity in joule per second.

Einstein’s mass-energy conversion:

$E=mc2$

Where, E is the energy release from the mass of m and c is speed of light.

Explanation:

Calculating the energy released mass-energy conversion of a carbon atom:

$E=mc2$

Replace $6×1024 kg$ for m and $3×108 m/s2$ for c in the above equation:

$E=(6×1024 kg)(3×108 m/s2)2=5.4×1041 J$

Recalling the expression for time:

$t=EL⊙$

Substituting $5.4×1041 J$ for $E$ and $3.90×1026 W$ for $L⊙$ in the above expression:

$t=5.4×1041 J3.90×1026 Jsecond =1.4×1015 seconds$

Conclusion:

The sun must shine for $1.4×1015 seconds$ to produce the energy produced by a substance with mass $6×1024 kg$ .

Answer 6

Chapter 16, Problem 9Q

(a)

To determine

The time for which the sun must shine in order to release energy produced by the mass-energy conversion of a carbon atom with mass $2×10−26 kg$ . The sun’s luminosity is $3.90×1026 W$ .

(a)

Expert Solution

Answer to Problem 9Q

Solution:

$4.6×10−36 s$

Explanation of Solution

Given data:

The sun’s luminosity is $3.90×1026 W$ , and the mass of carbon atom is $2×10−26 kg$ .

Formula used:

Time taken in seconds is given as:

$t=EL⊙$

Here, $E$ is the energy released due to mass-energy equivalence in joule and $L⊙$ is the luminosity in joule per second.

Einstein’s mass-energy conversion:

$E=mc2$

Where, E is the energy release from the mass of m and c is speed of light.

Explanation:

Calculating the energy released mass-energy conversion of a carbon atom:

$E=mc2$

Replace $2×10−26 kg$ for m and $3×108 m/s2$ for c in the above equation:

$E=(2×10−26 kg)(3×108 m/s2)2=1.8×10−9 J$

Recalling the expression for time:

$t=EL⊙$

Substituting $1.8×10−9 J$ for $E$ and $3.90×1026 W$ for $L⊙$ in the above expression:

$t=1.8×10−9 J3.90×1026 Jsecond =4.6×10−36 seconds$

Conclusion:

The sun must shine $4.6×10−36 s$ to produce the energy produced by a carbon atom with mass $2×10−26 kg$ .

Answer 7

Chapter 16, Problem 9Q

(a)

To determine

The time for which the sun must shine in order to release energy produced by the mass-energy conversion of a carbon atom with mass $2×10−26 kg$ . The sun’s luminosity is $3.90×1026 W$ .

Answer 8

(a)

Expert Solution

Answer to Problem 9Q

Solution:

$4.6×10−36 s$

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Given data:

The sun’s luminosity is $3.90×1026 W$ , and the mass of carbon atom is $2×10−26 kg$ .

Formula used:

Time taken in seconds is given as:

$t=EL⊙$

Here, $E$ is the energy released due to mass-energy equivalence in joule and $L⊙$ is the luminosity in joule per second.

Einstein’s mass-energy conversion:

$E=mc2$

Where, E is the energy release from the mass of m and c is speed of light.

Explanation:

Calculating the energy released mass-energy conversion of a carbon atom:

$E=mc2$

Replace $2×10−26 kg$ for m and $3×108 m/s2$ for c in the above equation:

$E=(2×10−26 kg)(3×108 m/s2)2=1.8×10−9 J$

Recalling the expression for time:

$t=EL⊙$

Substituting $1.8×10−9 J$ for $E$ and $3.90×1026 W$ for $L⊙$ in the above expression:

$t=1.8×10−9 J3.90×1026 Jsecond =4.6×10−36 seconds$

Conclusion:

The sun must shine $4.6×10−36 s$ to produce the energy produced by a carbon atom with mass $2×10−26 kg$ .

Answer 13

(b)

To determine

The time for which the sun must shine in order to release energy produced by the mass-energy conversion of 1 kg substance. The sun’s luminosity is $3.90×1026 W$ .

(b)

Expert Solution

Answer to Problem 9Q

Solution:

$2.3×10−10 s$

Explanation of Solution

Given data:

The sun’s luminosity is $3.90×1026 W$ , and the mass of the substance is 1 kg.

Formula used:

Time taken in seconds is given as:

$t=EL⊙$

Here, $E$ is the energy released due to mass-energy equivalence in joule and $L⊙$ is the luminosity in joule per second.

Einstein’s mass-energy conversion:

$E=mc2$

Where, E is the energy release from the mass of m and c is speed of light.

Explanation:

Calculating the energy released mass-energy conversion of a carbon atom:

$E=mc2$

Replace $1 kg$ for m and $3×108 m/s2$ for c in the above equation:

$E=(1 kg)(3×108 m/s2)2=9×1016 J$

Recalling the expression for the time:

$t=EL⊙$

Substituting $9.1×1016 J$ for $E$ and $3.90×1026 W$ for $L⊙$ in the above expression:

$t=9.1×1016 J 3.90×1026 Jsecond =2.3×10−10 seconds$

Conclusion:

The sun must shine for $2.3×10−10 seconds$ to produce the energy produced by a substance with mass $1 kg$ .

Answer 14

(b)

To determine

The time for which the sun must shine in order to release energy produced by the mass-energy conversion of 1 kg substance. The sun’s luminosity is $3.90×1026 W$ .

Answer 15

(b)

Expert Solution

Answer to Problem 9Q

Solution:

$2.3×10−10 s$

Answer 16

(b)

Expert Solution

Answer 17

(b)

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Given data:

The sun’s luminosity is $3.90×1026 W$ , and the mass of the substance is 1 kg.

Formula used:

Time taken in seconds is given as:

$t=EL⊙$

Here, $E$ is the energy released due to mass-energy equivalence in joule and $L⊙$ is the luminosity in joule per second.

Einstein’s mass-energy conversion:

$E=mc2$

Where, E is the energy release from the mass of m and c is speed of light.

Explanation:

Calculating the energy released mass-energy conversion of a carbon atom:

$E=mc2$

Replace $1 kg$ for m and $3×108 m/s2$ for c in the above equation:

$E=(1 kg)(3×108 m/s2)2=9×1016 J$

Recalling the expression for the time:

$t=EL⊙$

Substituting $9.1×1016 J$ for $E$ and $3.90×1026 W$ for $L⊙$ in the above expression:

$t=9.1×1016 J 3.90×1026 Jsecond =2.3×10−10 seconds$

Conclusion:

The sun must shine for $2.3×10−10 seconds$ to produce the energy produced by a substance with mass $1 kg$ .

Answer 20

(c)

To determine

The time for which the sun must shine in order to release energy, produced by the mass-energy conversion of Earth with mass $6×1024 kg$ . The sun’s luminosity is $3.90×1026 W$ .

(c)

Expert Solution

Answer to Problem 9Q

Solution:

$1.4×1015 seconds$

Explanation of Solution

Given data:

The sun’s luminosity is $3.90×1026 W$ , and the mass of Earth is $6×1024 kg$ .

Formula used:

Time taken in seconds is given as:

$t=EL⊙$

Here, $E$ is the energy released due to mass-energy equivalence in joule and $L⊙$ is the luminosity in joule per second.

Einstein’s mass-energy conversion:

$E=mc2$

Where, E is the energy release from the mass of m and c is speed of light.

Explanation:

Calculating the energy released mass-energy conversion of a carbon atom:

$E=mc2$

Replace $6×1024 kg$ for m and $3×108 m/s2$ for c in the above equation:

$E=(6×1024 kg)(3×108 m/s2)2=5.4×1041 J$

Recalling the expression for time:

$t=EL⊙$

Substituting $5.4×1041 J$ for $E$ and $3.90×1026 W$ for $L⊙$ in the above expression:

$t=5.4×1041 J3.90×1026 Jsecond =1.4×1015 seconds$

Conclusion:

The sun must shine for $1.4×1015 seconds$ to produce the energy produced by a substance with mass $6×1024 kg$ .

Answer 21

(c)

To determine

The time for which the sun must shine in order to release energy, produced by the mass-energy conversion of Earth with mass $6×1024 kg$ . The sun’s luminosity is $3.90×1026 W$ .

Answer 22

(c)

Expert Solution

Answer to Problem 9Q

Solution:

$1.4×1015 seconds$

Answer 23

(c)

Expert Solution

Answer 24

(c)

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

Given data:

The sun’s luminosity is $3.90×1026 W$ , and the mass of Earth is $6×1024 kg$ .

Formula used:

Time taken in seconds is given as:

$t=EL⊙$

Here, $E$ is the energy released due to mass-energy equivalence in joule and $L⊙$ is the luminosity in joule per second.

Einstein’s mass-energy conversion:

$E=mc2$

Where, E is the energy release from the mass of m and c is speed of light.

Explanation:

Calculating the energy released mass-energy conversion of a carbon atom:

$E=mc2$

Replace $6×1024 kg$ for m and $3×108 m/s2$ for c in the above equation:

$E=(6×1024 kg)(3×108 m/s2)2=5.4×1041 J$

Recalling the expression for time:

$t=EL⊙$

Substituting $5.4×1041 J$ for $E$ and $3.90×1026 W$ for $L⊙$ in the above expression:

$t=5.4×1041 J3.90×1026 Jsecond =1.4×1015 seconds$

Conclusion:

The sun must shine for $1.4×1015 seconds$ to produce the energy produced by a substance with mass $6×1024 kg$ .

Answer 27

Ch. 16 - Prob. 1CC Ch. 16 - Prob. 2CC Ch. 16 - Prob. 3CC Ch. 16 - Prob. 4CC Ch. 16 - Prob. 5CC Ch. 16 - Prob. 6CC Ch. 16 - Prob. 7CC Ch. 16 - Prob. 8CC Ch. 16 - Prob. 9CC Ch. 16 - Prob. 10CC

The time for which the sun must shine in order to release energy produced by the mass-energy conversion of a carbon atom with mass 2 × 10 − 26 kg . The sun’s luminosity is 3.90 × 10 26 W .

Concept explainers

The time for which the sun must shine in order to release energy produced by the mass-energy conversion of a carbon atom with mass $2×10−26 kg$ . The sun’s luminosity is $3.90×1026 W$ .

Answer to Problem 9Q

Explanation of Solution

The time for which the sun must shine in order to release energy produced by the mass-energy conversion of 1 kg substance. The sun’s luminosity is $3.90×1026 W$ .

Answer to Problem 9Q

Explanation of Solution

The time for which the sun must shine in order to release energy, produced by the mass-energy conversion of Earth with mass $6×1024 kg$ . The sun’s luminosity is $3.90×1026 W$ .

Answer to Problem 9Q

Explanation of Solution

Want to see more full solutions like this?

Chapter 16 Solutions

The time for which the sun must shine in order to release energy produced by the mass-energy conversion of a carbon atom with mass 2 × 10 − 26 kg . The sun’s luminosity is 3.90 × 10 26 ​ W .

Concept explainers

Answer to Problem 9Q

Explanation of Solution

Answer to Problem 9Q

Explanation of Solution

Answer to Problem 9Q

Explanation of Solution

Want to see more full solutions like this?

Chapter 16 Solutions

The time for which the sun must shine in order to release energy produced by the mass-energy conversion of a carbon atom with mass 2 × 10 − 26 kg . The sun’s luminosity is 3.90 × 10 26 W .