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Question

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) D2B
(b) CB+A
(c) B2A

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 MeV
Total binding energy for B, EB=8.5×60=510 MeV
Total binding energy for C, EC=8×90=720 MeV
Total binding energy for D, ED=7×120=840 MeV

Now, consider difference of final and initial energies for each of the reactions.
Reaction (a):
D2B
ΔE=2EBED=2×510840=180 MeV
ΔE>0 energy is absorbed

Reaction (b):
CB+A
ΔE=EB+EAEC=510+150720=60 MeV
ΔE<0 energy is released

Reaction (c):
B2A
ΔE=2EAEB=2×150510=210 MeV
ΔE<0 energy is released

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