1. What is Mass-Energy Equivalence?

The equation \( E = mc^2 \) represents the mass-energy equivalence principle from Einstein's theory of relativity. In nuclear reactions, small amounts of mass are converted to large amounts of energy.

2. How Does the Calculator Work?

The calculator uses Einstein's mass-energy equivalence formula:

Where:

• \( E \) — Energy released (Joules)
• \( \Delta m \) — Mass defect (difference between initial and final mass, in kg)
• \( c \) — Speed of light (299,792,458 m/s)

For nuclear fusion of hydrogen to helium, the mass defect per reaction is approximately 0.0048 atomic mass units (7.97 × 10⁻³⁰ kg).

3. Nuclear Fusion Context

Details: When 2 hydrogen atoms fuse to form 1 helium atom, about 0.7% of the mass is converted to energy. This powers stars and could be a future clean energy source.

4. Using the Calculator

Tips: Enter the mass defect in kilograms (1 atomic mass unit = 1.660539 × 10⁻²⁷ kg). Optionally enter moles of reactions (1 mole = 6.022 × 10²³ reactions).

5. Frequently Asked Questions (FAQ)

Q1: What's the mass defect for hydrogen fusion?
A: For 2H → He fusion, Δm ≈ 0.0048 u (7.97 × 10⁻³⁰ kg) per reaction, releasing ~4.3 × 10⁻¹² J.

Q2: How much energy per mole of fusion?
A: 1 mole of H→He reactions releases ~2.6 × 10¹² J (equivalent to ~600 tons of TNT).

Q3: Why is the energy release so large?
A: Because c² is an enormous number (9 × 10¹⁶ m²/s²), so tiny mass defects produce huge energy.

Q4: How does this relate to stars?
A: The Sun converts ~600 million tons of H to He each second, with 4 million tons becoming energy.

Q5: What's the efficiency of mass-energy conversion?
A: Nuclear fusion converts about 0.7% of mass to energy, compared to ~0.0000001% for chemical reactions.