(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? (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: $$ { }_{1}^{2} \mathrm{H}+{ }_{1}^{2} \mathrm{H} \rightarrow{ }_{2}^{3} \mathrm{He}+{ }_{0}^{1} \mathrm{n} $$ Is this reaction exothermic or endothermic? Calculate its $Q$ value.

(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? (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:
$$
{ }_{1}^{2} \mathrm{H}+{ }_{1}^{2} \mathrm{H} \rightarrow{ }_{2}^{3} \mathrm{He}+{ }_{0}^{1} \mathrm{n}
$$
Is this reaction exothermic or endothermic? Calculate its
$Q$ value.

Key Concepts

Q Value Calculation

This concept involves determining the energy released or absorbed in a nuclear reaction by calculating the difference in the total mass of the reacting nuclei (reactants) and the resulting nuclei (products), and then converting this mass difference into energy using Einstein's equation, E=mc². A positive Q value indicates an exothermic reaction where energy is released, while a negative value indicates an endothermic reaction where energy is absorbed.

Mass Defect

The mass defect is the difference between the mass of a nucleus and the sum of the individual masses of its protons and neutrons. This 'lost' mass is the binding energy that holds the nucleus together. The mass defect is a key factor in calculating the Q value of a nuclear reaction because it shows how much energy is released or absorbed when the nucleus is formed or broken apart.

Exothermic and Endothermic Reactions

These terms describe the energy balance in a nuclear reaction. An exothermic reaction releases energy, meaning that the mass of the reactants is greater than that of the products, leading to a positive Q value. Conversely, an endothermic reaction requires an input of energy because the mass of the products exceeds the mass of the reactants, resulting in a negative Q value.

Mass-Energy Equivalence

This principle, encapsulated in Einstein’s famous equation E=mc², relates mass to energy and is fundamental in nuclear physics. It explains how small differences in mass (due to the mass defect) can be converted into large amounts of energy, a concept that is crucial for understanding the energy changes that occur in nuclear reactions.

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