Question

The binding energy per nucleon of ${}_1{H}^2$ and ${}_{2}H{e}^4$ are $1.1MeV$ and $7MeV$, respectively. If two deuteron nuclei react to form a single helium nucleus, then the energy released is :

• A. $13.9MeV$
• B. $26.9MeV$
• C. $23.6MeV$
• D. $19.2MeV$

Answer 1

The correct option is C $23.6MeV$

The binding energy per nucleon of ${}_1{H}^2$ and ${}_{2}H{e}^4$ are $1.1MeV$ and $7MeV$, respectively.
${}_1{H}^2$ and ${}_{2}H{e}^4$ contain 2 and 4 nucleons respectively.
The binding energy for ${}_1{H}^2$ and ${}_{2}H{e}^4$ is $2\times 1.1MeV$

$=2.2MeV$ and $4\times 7MeV$

$=28MeV$ respectively.
If two deuteron nuclei react to form a single helium nucleus, then the energy released is,

$28MeV-2\times 2.2MeV$

$=23.6MeV$.