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

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 $A,E_A=5\times 30=150MeV$

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