Physics

Problem

(a) Define the Q–value of a nuclear reaction. (b) A nuclear reaction is said to be exothermic when it releases energy and endothermic when it absorbs energy. Explain, without performing any numerical calculation, how the relative total masses of the reactants and products decide whether the reaction is exothermic or endothermic. (c) Two reactions are listed below: (i)

_1^2\text H +\;_1^2\text H \;\longrightarrow\;_2^3\text{He}+\;_0^1\text n

(ii)

_0^1\text n +\;_{92}^{235}\text U\;\longrightarrow\;_{36}^{92}\text{Kr}+\;_{56}^{141}\text{Ba}+3\,_0^1\text n

Using qualitative reasoning based on binding–energy per nucleon and mass–energy equivalence, discuss which of the above reactions releases more energy per nucleon. (d) State any two practical consequences of the sign and magnitude of the Q–value in nuclear engineering applications. (i)

\,_{1}^{2}\text{H} + \;_{1}^{2}\text{H} \;\longrightarrow\; \;_{2}^{3}\text{He} + \;_{0}^{1}\text{n}

(ii)

\,_{0}^{1}\text{n} + \;_{92}^{235}\text{U}\;\longrightarrow\; \;_{36}^{92}\text{Kr} + \;_{56}^{141}\text{Ba} + 3\,_{0}^{1}\text{n}

Using qualitative reasoning based on binding–energy per nucleon and mass–energy equivalence, discuss which of the above reactions releases more energy per nucleon.

Intuitive explanation

The Q-value captures the energy released or absorbed in a nuclear reaction through mass-energy equivalence: it's the difference between the rest mass energy of reactants and products. Since mass can convert to energy (via $E=mc^2$ ), a reaction's energetics hinge entirely on whether the initial or final particles weigh more—the "missing mass" becomes kinetic energy or heat. Understanding this connection between mass defect and energy release is the key to predicting whether a reaction powers itself or needs external energy.

Intuitive explanation

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