Question

The atomic mass of ${}^{16}O$ is 15.995$m_u$ while the individual masses of proton and neutron are 1.0073 and 1.0087$m_u$. The mass of electron = 0.000548$m_u$. Calculate the binding energy of the oxygen nucleus in joules.

• A. $1.232\times {10}^{13}Jmo{l}^{-1}$
• B. $3.232\times {10}^{13}Jmo{l}^{-1}$
• C. $2.222\times {10}^{13}Jmo{l}^{-1}$
• D. None of these

Answer 1

The correct option is A $1.232\times {10}^{13}Jmo{l}^{-1}$

$Massdefect=15.995-\left[8\right(1.0073+1.0087+0.000548\left)\right]$
$=15.995+16.132384=0.137384units$
$\therefore BE=0.137884\times 931MeV$
$=127.9045MeV$
$=127.90450\times {10}^{6}eV$
$=127.9045\times {10}^8\times 1.6\times {10}^{-19}J$
$=2.046\times {10}^{-11}J$ per molecule
$=2.046\times {10}^{-11}\times 6.02\times {10}^{23}$
$=1.232\times {10}^{13}Jmo{l}^{-1}$