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) $D\to 2B$
(b) $C\to B+A$
(c) $B\to 2A$

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