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# Mass numbers of the elements A, B, C and D are 30, 60, 90 and 120 respectively. The specific binding energy of them are 5MeV, 8.5MeV, 8MeV and 7MeV respectively. Then, in which of the following reaction/s energy is released?(a) D→2B(b) C→B+A(c) B→2A

A
Only in (a)
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B
In (b), (c)
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C
In (a), (c)
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D
In (a), (b) and (c)
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Solution

## The correct option is B In (b), (c)Total binding energy equals the product of binding energy per nucleon and mass number.Total binding energy for A, EA=5×30=150 MeVTotal binding energy for B, EB=8.5×60=510 MeVTotal binding energy for C, EC=8×90=720 MeVTotal binding energy for D, ED=7×120=840 MeVNow, consider difference of final and initial energies for each of the reactions.Reaction (a):D→2BΔE=2EB−ED=2×510−840=180 MeVΔE>0⟹ energy is absorbedReaction (b):C→B+AΔE=EB+EA−EC=510+150−720=−60 MeVΔE<0⟹ energy is releasedReaction (c):B→2AΔE=2EA−EB=2×150−510=−210 MeVΔE<0⟹ energy is released

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