Question

The binding energy per nucleon of oxygen atom $ _{8}O^{16} $ , which has a mass $15.994910 \,u$ is : (mass of neutron $= 1.008665$, mass of proton $= 1.007277 \,u$, mass of electron $= 0.0005486 \,u$) is

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

Answer 1

Answer: (A)

Binding energy $=\Delta M \times 931\, MeV$
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 $8 n+$ mass of $8 e^{-}$
$=8 \times 1.007277+8 \times 1.008665 $
$+8 \times 0.0005486 $
$=16.1319248 \,u$
Mass defect $(\Delta M) =M'-M $
$=16.1319248 $
$=0.1370148 \,u $
Binding energy $=0.1370148 \times 931 \,MeV $
$=127.62 \,MeV $
$\because $ Number of nucleons in ${ }_{8}^{16} O =16 $
$ \therefore $ Binding energy per nucleon $=\frac{127.62}{16} MeV$
$=7.976 \,MeV$