For The Following Fusion Reaction Calculate The Chnage Inm Energy

Introduction

Fusion reactions are nuclear processes where lighter atomic nuclei combine to form heavier nuclei, releasing a significant amount of energy. According to Einstein's mass-energy equivalence principle, this energy release is directly related to the change in mass during the reaction.

The calculator uses the formula E = Δmc², where E is the energy released, Δm is the change in mass, and c is the speed of light. This tool provides a straightforward way to calculate the energy output from a fusion reaction.

Formula

Where:

• E = Energy released (in joules, J)
• Δm = Change in mass (in kilograms, kg)
• c = Speed of light (approximately 2.99792458 × 10⁸ m/s)

The formula shows that energy is directly proportional to the change in mass and the square of the speed of light. This means even small changes in mass result in large energy releases, which is why fusion reactions are so powerful.

Calculation Process

To calculate the energy released from a fusion reaction:

1. Determine the change in mass (Δm) between the initial reactants and final products.
2. Square the speed of light (c²).
3. Multiply the change in mass by c² to get the energy released.

This calculation is based on the principle that mass and energy are interchangeable, as described by Einstein's famous equation E=mc².

Worked Example

Consider a fusion reaction where 1.67 × 10⁻²⁷ kg of mass is converted to energy. Using the formula:

Calculating this gives approximately 2.46 × 10⁻¹³ joules of energy released. This demonstrates how even small changes in mass result in significant energy outputs.