Question

What is the binding energy of ${ }^{29} Si_{14}$ whose atomic $14$
mass is $28.976495\, u$
Mass of proton $=1.007276\, u$
Mass of neutron $=1.008664\, u$
$($ Neglect the electron mass $)$
(Assume $1 \,u =931.5\,MeV$ )

• A. 237.84 MeV
• B. 421.72 MeV
• C. 387.21 MeV
• D. 116.35 MeV

Answer 1

Answer: (A)

Given, mass of ${ }_{14}{ }^{29} S i=28.976495 u$
Now, mass of $14$ protons
$=14 \times$ mass of $1 $ proton
$=14 \times 1.007276=14.101864 u$
Also, mass of $29-14=15$ neutrons
$=15 \times$ mass of $1$ neutron
$=15 \times 1.008664=15.12996$
Total mass of constituents of $S i$ atom
$=14.101864+15.12996=29.231824$
So, mass defect $=$ mass of constituents $-$ mass of atom
$=29.231824-28.976495=0.255329\, u$
Binding energy $=$ Energy equivalent of mass defect
$=\Delta M \times 931.5 MeV$
$=0.255329 \times 931.5=237.84\, MeV$