Mass–Energy Equivalence | CAIE 9702 Paper 4 Notes

Paper 4

Physics9702

Compare every particle before and after

Mass and energy are two ways of measuring the total energy of a system. Here rest mass means the mass measured when the system as a whole is at rest. When energy leaves a system, its rest mass decreases. The mass has not disappeared; the decrease corresponds to the transferred energy.

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Compare the same complete system before and after the reaction. If the final rest mass is smaller, the positive mass decrease corresponds to energy released.

A rest mass $m$ has an equivalent rest energy $E$ .

E=mc^2

A reaction calculation compares two complete states, so it uses the change in mass and the corresponding change in energy.

Key idea

Define the mass decrease using the complete initial and final systems. A positive decrease gives a positive released energy.

\Delta m=m_{\mathrm{initial}}-m_{\mathrm{final}}

\Delta E=\Delta m c^2

Symbols

$\Delta E$ = energy released by the mass decrease (J)
$\Delta m$ = initial mass minus final mass (kg)
$c$ = speed of light in vacuum, 3.00 × 10⁸ (m s⁻¹)

Worked example

Energy from a small mass decrease

The total rest mass decreases by $3.2\times10^{-28}$ kg. Calculate the energy released.

Use the positive mass decrease because the question asks for energy released.
$\begin{aligned}\Delta E&=(3.2\times10^{-28})\\&\quad\times(3.00\times10^8)^2\end{aligned}$
$\Delta E=2.88\times10^{-11}\ \mathrm{J}$

Answer

2.9\times10^{-11}\ \mathrm{J}

Your turnconcept check

A reaction releases energy. Is the total rest mass before the reaction greater than or less than the total rest mass after it?

Show worked answer

It is greater before the reaction. The decrease in total rest mass corresponds to the energy released.