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 $5 \, MeV, 8.5 \, MeV, 8 \, MeV$ and $7 \, MeV$ respectively. Then, in which of the following reaction/s energy is released ?
(a) $D \rightarrow 2B$
(b) $C \rightarrow B + A$
(c) $B \rightarrow 2 A$

• A. only in (a)
• B. in (b), (c)
• C. in (a), (c)
• D. in (a), (b) and (c)

Answer 1

Answer: (B)

Total binding energy for $A , E _{ A }=5 \times 30=150 MeV$
Total binding energy for $B , E _{ B }=8.5 \times 60=510 MeV$
Total binding energy for $C , E _{ C }=8 \times 90=720 MeV$
Total binding energy for $D , E _{ D }=7 \times 120=840 MeV$
Now, consider difference of final and initial energies for each of the reactions.
Reaction (a):
$D \rightarrow 2 B$
$\Delta E =2 E _{ B }- E _{ D }=2 \times 510-840=180 MeV$
$\Delta E >0 \Longrightarrow$ energy is absorbed
Reaction (b):
$C \rightarrow B + A$
$\Delta E = E _{ B }+ E _{ A }- E _{ C }=510+150-720=-60 MeV$
$\Delta E <0 \Longrightarrow$ energy is released
Reaction (c):
$B \rightarrow 2 A$
$\Delta E =2 E _{ A }- E _{ B }=2 \times 150-510=-210 MeV$
$\Delta E <0 \Longrightarrow$ energy is released