ELECTROMAGNETISM & RELATIVITY - Chapter 9, Exercise 1 Solution
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Rest Energy of 0.5 Grams

PROBLEM
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Calculate the rest energy of 5 x 10^-4 kg (0.5 g) of matter, using
E = mc^2.

SOLUTION
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Using the rest-energy formula:

    E = m c^2

Substitute the given values:

    m = 5 x 10^-4 kg
    c = 3 x 10^8 m/s

    E = (5 x 10^-4) x (3 x 10^8)^2
    E = (5 x 10^-4) x (9 x 10^16)
    E = 4.5 x 10^13 J

ANSWER: The rest energy of 0.5 g of matter is approximately
4.5 x 10^13 J.

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WHY THIS WORKS AS AN ANSWER

This result is, as expected, exactly half of the chapter's own 1 g
worked example (which gave approximately 9 x 10^13 J), since rest
energy scales directly and linearly with mass - halving the mass
exactly halves the energy. The genuinely striking part of this result
is not the calculation itself but the scale: half a gram of ordinary
matter, an amount too small to feel meaningfully on a kitchen scale,
carries tens of trillions of joules of energy locked inside it via
E = mc^2 - energy that stays completely inert and unreleased unless a
real physical process (like the nuclear fission covered in the
chapter) actually converts some of that mass.