The sun radiates energy at the rate 3.8 x 10²⁶ W. The source of this energy is fusion, a nuclear reaction in which mass is transformed into energy. The mass of the sun is 2.0 x 10³⁰ kg. What percent is this of the sun's total mass?

Verified step by step guidance

1. Determine the energy radiated by the sun per second, which is given as 3.8 × 10^26 W. Recall that power (P) is the rate of energy transfer per unit time.
2. Use Einstein's mass-energy equivalence formula, E = mc^2, to calculate the mass equivalent of the energy radiated. Rearrange the formula to find m = E / c^2, where c is the speed of light (approximately 3.0 × 10^8 m/s).
3. Substitute the energy radiated per second (E = 3.8 × 10^26 J) and the speed of light (c = 3.0 × 10^8 m/s) into the equation m = E / c^2 to calculate the mass lost per second.
4. To find the percentage of the sun's total mass lost, divide the mass lost per second by the total mass of the sun (2.0 × 10^30 kg) and multiply by 100%. Use the formula: percentage = (mass lost / total mass) × 100%.
5. Simplify the expression to determine the percentage of the sun's total mass that is converted into energy per second. Ensure all units are consistent and calculations are performed step by step.

Key Concepts

Energy-Mass Equivalence

Energy-mass equivalence is a principle derived from Einstein's theory of relativity, encapsulated in the equation E=mc². This concept states that mass can be converted into energy and vice versa, highlighting the relationship between mass and energy. In the context of the sun, this principle explains how the mass lost during nuclear fusion is transformed into the energy radiated by the sun.

Nuclear Fusion

Nuclear fusion is a process where two light atomic nuclei combine to form a heavier nucleus, releasing a significant amount of energy in the process. This reaction powers stars, including the sun, where hydrogen nuclei fuse to form helium. Understanding fusion is crucial for calculating the energy output of the sun and its implications for mass loss over time.

Percentage Calculation

Percentage calculation is a mathematical process used to express a number as a fraction of 100. In this context, it involves determining what fraction of the sun's total mass is converted into energy. This requires dividing the mass equivalent of the energy output by the sun's total mass and multiplying by 100 to obtain the percentage, providing insight into the efficiency of the sun's energy production.