Calculating Nuclear Reaction Energy | CAIE 9702 Paper 4 Notes

Paper 4

Physics9702

Convert u before using SI units

Nuclear masses are often given in the atomic mass unit, $u$ . The mass–energy equation gives joules only when the mass difference is first converted to kilograms.

1\ \mathrm{u}=1.66\times10^{-27}\ \mathrm{kg}

Your turnfoundation calculation

A reaction has a mass decrease of 0.0030 u. Calculate the energy released in joules.

Show worked answer

\Delta m=(0.0030)(1.66\times10^{-27})

\Delta E=\Delta mc^2

c^2=9.00\times10^{16}\ \mathrm{m^2\,s^{-2}}

\Delta E=4.5\times10^{-13}\ \mathrm{J}

The energy released is $4.5\times10^{-13}\ \mathrm{J}$ .

Calculate one reaction before scaling up

Worked example

Energy from deuterium fusion

Two deuterium nuclei, each of mass 2.013 553 u, form one helium-4 nucleus of mass 4.001 505 u. Calculate the energy released when 1.00 mol of helium-4 forms (9702/42/O/N/25 Q9(b)).

Find the mass decrease for one reaction.
$m_{\mathrm{initial}}=2(2.013553)\ \mathrm{u}$
$m_{\mathrm{final}}=4.001505\ \mathrm{u}$
$\Delta m=0.025601\ \mathrm{u}$
Convert to kilograms by multiplying 0.025 601 by $1.66\times10^{-27}$ .
$\Delta m=4.25\times10^{-29}\ \mathrm{kg}$
Find the energy for one helium-4 nucleus.
$\Delta E=\Delta m(3.00\times10^8)^2$
$\Delta E=3.82\times10^{-12}\ \mathrm{J}$
Multiply by the Avogadro constant for one mole.
$E_{\mathrm{mol}}=E_{\mathrm{one}}N_A$
$\begin{aligned}E_{\mathrm{mol}}&=(3.82\times10^{-12})\\&\quad\times(6.02\times10^{23})\end{aligned}$

Answer

2.30\times10^{12}\ \mathrm{J}

Common mistake

Compare like with like. If the data give atomic masses, electron masses must cancel consistently. If the data give nuclear masses, use nuclear masses throughout. Never mix the two systems without accounting for the electrons.