The above is a plot of binding energy per nucleon \(\mathrm{E}_{\mathrm{b}}\), against the nuclear mass \(\mathrm{M} ; \mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}, \mathrm{E}, \mathrm{F}\) correspond to different nuclei. Consider four reactions: (i) \(\mathrm{A}+\mathrm{B} \rightarrow \mathrm{C}+\varepsilon\) (ii) \(\mathrm{C} \rightarrow \mathrm{A}+\mathrm{B}+\varepsilon\) (iii) \(D+E \rightarrow F+\varepsilon\) and (iv) \(\mathrm{F} \rightarrow \mathrm{D}+\mathrm{E}+\varepsilon\) where \(\varepsilon\) is the energy released? In which reactions is \(\varepsilon\) positive?

JEE Main · 2009 · 12 Apr 2009 · Offline · Modern Physics

The above is a plot of binding energy per nucleon

E_{b}

, against the nuclear mass

M; A, B, C, D, E, F

correspond to different nuclei. Consider four reactions:
(i)

A + B \to C + ε

(ii)

C \to A + B + ε

(iii)

D + E \to F + ε

and
(iv)

F \to D + E + ε

where

ε

is the energy released? In which reactions is

ε

positive?

(A)(i) and (iv)✓ Correct
(B)(i) and (iii)
(C)(ii) and (iv)
(D)(ii) and (iii)

Answer: (A)

Solution

Energy is released only when the products sit higher on the binding-energy-per-nucleon curve than the reactants, because greater binding energy per nucleon means a more tightly bound, lower-energy state. Light nuclei A and B fusing into C climb the rising part of the curve and so release energy, and the heavy nucleus F splitting into D and E moves up the falling part of the curve and likewise releases energy. These are the first and fourth reactions.

JEE Main · 2009 · 12 Apr 2009 · Offline · Single correct option

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JEE Main · 2009 · 12 Apr 2009 · Offline · Modern Physics

Solution

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