Question

Consider the following nuclear reaction:
$X^{200}\to A^{110}+B^{90}+Energy$
If the binding energy per nucleon for $X$, $A$ and $B$ are $7.4MeV$, $8.2MeV$ and $8.2MeV$ respectively, the energy released will be:

• A. $90MeV$
• B. $110MeV$
• C. $200MeV$
• D. $160MeV$

Answer 1

The correct option is D $160MeV$

Binding energy of $X$: $E_X=200\times 7.4=1480MeV$

Binding energy of $A$: $E_A=110\times 8.2=902MeV$

Binding energy of $B$: $E_B=90\times 8.2=738MeV$

$\therefore$ energy released, $E=E_A+E_B-E_X=902+738-1480=160MeV$