If 1.8x1014 J are given off in a nuclear reaction, how much matter is converted into energy? Not a clue as to how I would even START to figure this one out - help!!!
To determine the amount of matter converted into energy in a nuclear reaction, you can use Albert Einstein's mass-energy equivalence formula, E = mc². This formula relates energy (E) to mass (m) and the speed of light (c). By rearranging the equation, you can calculate the mass that corresponds to a given amount of energy. Here's how you can approach the problem:
1. Start by identifying the given values:
Energy (E) = 1.8x10^14 J (joules)
2. Use the mass-energy equivalence formula to calculate the mass (m):
E = mc²
Rearrange the equation to solve for mass (m):
m = E / c²
The speed of light (c) is approximately 3x10^8 m/s, so the equation becomes:
m = E / (3x10^8)^2
3. Substitute the given energy value into the equation:
m = (1.8x10^14 J) / (3x10^8 m/s)²
4. Calculate the mass:
m = (1.8x10^14 J) / (9x10^16 m²/s²)
Simplifying the equation, you get:
m = 2x10^(-2) kg
Therefore, approximately 0.02 kilograms of matter are converted into energy in this nuclear reaction.
Use E = mc^2.
You know E and c. Solve for m.