Question

The binding energy per nucleon of oxygen atom ${}_8{O}^{16}$ , which has a mass $15.994910u$ is : (mass of neutron $=1.008665$, mass of proton $=1.007277u$, mass of electron $=0.0005486u$) is

• A. 7.976 MeV
• B. 8.542 MeV
• C. 6.62 MeV
• D. 931 MeV

Answer 1

Answer: (A)

Binding energy $=\Delta M\times 931MeV$
Binding energy per nucleon
$=\frac{\text{ total binding energy }}{\text{ number of nucleons }}$
${}_8^{16}O$ contain $8$ protons, $8$ neutrons and $8$
electrons.
Hence, mass of ${}_8^{16}O=$ mass of $8$ protons + mass of $8n+$ mass of $8e^{-}$
$=8\times 1.007277+8\times 1.008665$
$+8\times 0.0005486$
$=16.1319248u$
Mass defect $(\Delta M)=M^{\prime }-M$
$=16.1319248$
$=0.1370148u$
Binding energy $=0.1370148\times 931MeV$
$=127.62MeV$
$\because$ Number of nucleons in ${}_8^{16}O=16$
$\therefore$ Binding energy per nucleon $=\frac{127.62}{16}MeV$
$=7.976MeV$