Question

The mass of proton is 1.0073 u and that of neutron is 1.0087 u (u = atomic mass unit). The binding energy of $^{4}_{2}He$ is Given, mass of helium nucleus $\approx4.0015 u.$

• A. 28.4 MeV
• B. 0.061 u
• C. 0.0305 J
• D. 0.0305 erg

Answer 1

Answer: (A)

28.4 MeV

Answer 2

$_2He^4$ contains 2 neutrons and 2 protons
Mass of 2 protons $=2 \times 1.0073$
$=2.0146 u$
Mass of 2 neutrons $=2 \times 1.0087$
$=2.0174 u$
Total mass of 2 protons and 2 neutrons
=(2.0146+ 2.0174)u =4.032u
Mass of helium nucleus= 4.0015 u
Thus, mass defect is lacking of mass in forming the helium
nucleus from 2 protons and 2 neutrons.
$\therefore ?m=mass \, defect$
$$ = ( 4.032 - 4.0015 )u
$$ = 0.0305 u
$$ = 0.0305amu
but $1 \, amu=931 MeV$
Hence, binding energy
$? E=(?m) \times 931$
$=0.0305 \times 931=28.4 MeV$