Question 13: Atoms & Nuclei

Question

The mass of proton is 1.0073 u and that of neutron is $1.0087 \mathrm{u}(\mathrm{u}=$ atomic mass unit). The binding energy of ${ }_2 \mathrm{He}^4$ is

Accepted Answer

The nucleus of ${ }_2 \mathrm{He}^4$ contains 2 neutrons and 2 protons.
Mass of 2 protons $=2 	imes 1.0073=2.0146 u$
Mass of 2 neutrons $=2 	imes 1.0087=2.0174 u$
Total mass of 2 protons and 2 neutrons
$$ =(2.0146+2.0174)=4.032 u $$
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.
$$ \begin{aligned} 	herefore \Delta m & =	ext { Mass defect } \ & =(4.032-4.0015) \mathrm{u}=0.0305 \mathrm{u} \ & =0.0305 \mathrm{amu} \end{aligned} $$
but $1 \mathrm{amu}=931 \mathrm{MeV}$
Hence, binding energy,
$$ \begin{aligned} \Delta E & =(\Delta m) 	imes 931 \ & =0.0305 	imes 931=28.4 \mathrm{MeV} \end{aligned} $$

Answer

28.4 MeV

Answer

0.061 u

Answer

0.0305 J

Answer

0.0305 erg

Atoms & Nuclei

The mass of proton is 1.0073 u and that of neutron is 1.0087 \mathrm{u}(\mathrm{u}= atomic mass unit). The binding energy of { }_2 \mathrm{He}^4 is

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