Find the energy equivalents of (a) an electron of mass 9.11...

Find the energy equivalents of (a) an electron of mass $9.11 \times 10^{-31} \mathrm{~kg}$, (b) a uranium atom with a mass of $4.00 \times 10^{-25} \mathrm{~kg},(\mathrm{c})$ a paper clip of mass $2.00 \mathrm{~g}$, and
(d) the Earth (of mass $5.99 \times 10^{24} \mathrm{~kg}$ ).

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Key Concepts

Unit Conversion and Order of Magnitude

When applying mass-energy equivalence to various objects, it is essential to convert and manipulate units properly, ensuring consistent usage of the International System of Units (SI). Understanding orders of magnitude is also crucial, as it helps put into perspective the vast differences in energy equivalence across objects ranging from subatomic particles to astronomical bodies.

Mass?Energy Equivalence

This concept states that mass and energy are interconvertible, as encapsulated by Einstein's famous equation E = mc². It implies that any mass has an equivalent amount of energy, which becomes particularly significant in nuclear physics and cosmology, where small amounts of mass can represent huge amounts of energy.

Einstein's Equation (E = mc²)

Einstein’s equation provides the mathematical relationship between mass and energy, where E represents energy, m is mass, and c is the speed of light in vacuum. This equation highlights that the energy stored in a mass is proportional to its quantity, with the speed of light squared acting as the conversion factor, making even a tiny mass capable of releasing tremendous energy.

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