IB Physics SL E.3.4 Mass-Energy Equivalence

Practise converting mass changes into nuclear energy with E = Δmc², calculating reaction Q values and assigning energy release or absorption from the sign of the mass difference.

Exam points

calculate Δm as initial mass minus final mass for a complete nuclear reaction
convert kilograms with c² or atomic mass units with 931.5 MeV u⁻¹ without mixing units
interpret positive Q as released energy and negative Q as the required threshold input

[Maximum number: 2]

This section consists of three questions: B1, B2 and B3.

Tritium may be produced by bombarding a nucleus of the isotope lithium-7 with a high-energy neutron. The reaction equation for this interaction is

{ }_{3}^{7} \mathrm{Li}+{ }_{0}^{1} \mathrm{n} \rightarrow{ }_{1}^{3} \mathrm{H}+{ }_{Z}^{4} \mathrm{X}+{ }_{0}^{1} \mathrm{n} .

Use the following data to show that the minimum energy that a neutron must have to initiate the reaction in (b)(i) is about 2.5 MeV .

\begin{array}{ll} \text { Rest mass of lithium-7 nucleus } & =7.0160 \mathrm{u} \\ \text { Rest mass of tritium nucleus } & =3.0161 \mathrm{u} \\ \text { Rest mass of X nucleus } & =4.0026 \mathrm{u} \end{array}

(mass difference $=) 7.0160-[3.0161+4.0026]=(-) 2.7 \times 10^{-3} \mathrm{u}$ ; ( energy required $=)(-) 2.7 \times 10^{-3} \times 931.5$ or 2.5151 MeV ; ( $\approx 2.5 \mathrm{MeV}$ )

Marking guidance:

Allow unit conversions via mass and $m c^{2}$ .

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E.3.4—Mass-energy equivalence question 1