Question

If four grams of matter are converted to their equivalent amount of energy, how much energy is released? Show your work.

Answer 1

Use Albert Einstein's equation

• E=mc²

m=0.004kg

• E=(0.004)(3×10⁸)²
• E=0.004(9×10¹⁶)
• E=3.6×10¹⁴J

Answer 2

Equation of Special Relativity

`E=mc^2`

where:

• E = energy (measured in Joules)
• m = mass (measured in kilograms)
• c = speed of light where
  `c \approx 3 * 10^8 \: \sf ms^(-1)`

First, convert 4 g into kilograms as mass is measured in kg:

`\implies \sf 4\:g = 0.004\:kg=4 * 10^(-3)\:kg`

Substitute the given values into the equation and solve for E:

`\begin{aligned}E & = mc^2\\\implies E & = \sf (4 * 10^(-3)) \cdot(3 * 10^8)^2\\& = \sf (4 * 10^(-3)) \cdot (3^2 * 10^(8(2)))\\& = \sf (4 * 10^(-3)) \cdot (9 * 10^(16))\\& = \sf 4 \cdot9 * 10^(-3) \cdot10^(16)\\& = \sf 36 * 10^((-3+16))\\& = \sf 36 * 10^(13)\\& = \sf 3.6 * 10^(14)\: \sf J \end{aligned}`