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
Only in (a)
In (b), (c)
In (a), (c)
In (a), (b) and (c)
A
In (a), (b) and (c)
B
In (a), (c)
C
Only in (a)
D
In (b), (c)
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Solution
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Total binding energy equals the product of binding energy per nucleon and mass number.
Total binding energy for A,EA=5×30=150MeV
Total binding energy for B,EB=8.5×60=510MeV
Total binding energy for C,EC=8×90=720MeV
Total binding energy for D,ED=7×120=840MeV
Now, consider difference of final and initial energies for each of the reactions.
Reaction (a):
D→2B
ΔE=2EB−ED=2×510−840=180MeV
ΔE>0⟹ energy is absorbed
Reaction (b):
C→B+A
ΔE=EB+EA−EC=510+150−720=−60MeV
ΔE<0⟹ energy is released
Reaction (c):
B→2A
ΔE=2EA−EB=2×150−510=−210MeV
ΔE<0⟹ energy is released
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