(a) One method of producing neutrons for experimental use is...

(a) One method of producing neutrons for experimental use is bombardment of light nuclei with alpha particles. In the method used by James Chadwick in $1932,$ alpha particles emitted by polonium are incident on beryllium nuclei: $$_{2}^{4} \mathrm{He}+_{4}^{9} \mathrm{Be} \rightarrow_{6}^{12} \mathrm{C}+_{0}^{1} \mathrm{n}$$ What is the $Q$ value of this reaction? (b) Neutrons are also often produced by small-particle accelerators. In one design, deuterons accelerated in a Van de Graaff generator bombard other deuterium nuclei and cause the reaction $$_{1}^{2} \mathrm{H}+_{1}^{2} \mathrm{H} \rightarrow_{2}^{3} \mathrm{He}+_{0}^{1}$$ Calculate the $Q$ value of the reaction. (c) Is the reaction in part (b) exothermic or endothermic?

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Key Concepts

Mass-Energy Equivalence

Mass-energy equivalence is the principle encapsulated by Einstein’s equation E=mc², which shows that mass and energy are interchangeable. In nuclear physics, small changes in mass during a reaction can result in significant energy changes, making it essential for calculating the Q value of nuclear reactions.

Q Value in Nuclear Reactions

The Q value is a measure of the net energy released or absorbed during a nuclear reaction, calculated using the mass difference between the reactants and products converted to energy via Einstein’s mass-energy equivalence (E=mc²). A positive Q value indicates that the reaction releases energy, while a negative Q value shows that energy is absorbed.

Exothermic and Endothermic Reactions

In nuclear physics, exothermic reactions are those that release energy (positive Q value) while endothermic reactions require an input of energy (negative Q value). This distinction is critical for understanding the feasibility of nuclear reactions and their applications in energy production or experimental setups.

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